What is the sign of a root judged by Vedic theorem?

Vedic theorem. It's the root relationship!

For quadratic equations.

ax^2+bx+c=0

A is not equal to 0).

to say x1+x2=-b a

x1*x2=c/a

If both roots of the equation are 0, then -b a>0 and x1*x2>0, conversely, if -b a>0 and x1*x2>0, then the equation has two positive and real roots!

If both roots of the equation < 0, then -b a<0 and x1*x2>0 conversely, if -b a<0 and x1*x2>0, then the equation has two negative real roots!

If the equation is two, one is one.

negative, and positive and absolute.

larger, then -b a>0 and x1*x2<0

On the other hand, if -b a>0 and x1*x2<0, the two roots of the equation are positive and negative, and the positive and absolute values are larger.

If the equation has two roots, one positive and one negative, and the absolute value of the negative roots is larger, then -b a<0 and x1*x2<0

On the other hand, if -b a<0 and x1*x2<0, the equation has two roots, one positive and one negative, and the negative and absolute values are larger.

You see, is it possible to judge the sign of the root just by using Veda's theorem?

via x1+x2=-b a

x1*x2=c/a

where x1x2

are the two roots of the equation, abc

is the coefficient of the equation ax 2 + bx + c = 0

Pass x1+x2

x1*x2 to determine the symbol of the two roots.

x1*x2>0

and x1 x2 0

This means that there are two positive roots.

x1*x2>0

and x1 x2 0

This means that there are two negative roots.

x1 x2 0 and x1 x2 0

Then there is one positive and one negative, and the absolute value of the positive number is negative.

x1 x2 0 and x1 x2 0

Then there is one positive and one negative, and the absolute value of the positive number is negative.

Hello! x1*x2>0

then the two roots have the same number.

Otherwise, it is a different name.

x1*x2>0

and x1 x2 0

This means that there are two positive roots.

x1*x2>0

and x1 x2 0

This means that there are two negative roots.

x1 x2 0 and x1 x2 0

Then there is one positive and one negative, and the absolute value of the positive number is negative.

x1 x2 0 and x1 x2 0

Then there is one positive and one negative, and the absolute value of the positive number is negative.

Hope it helps, hopefully.

Vedic car Min theorem x1+x2=-b a x1x2=c a discriminant of the equation a δ=b squared which family -4ac

The equation has two unequal real roots.

The 0 equation has two equal real roots.

That's a very good question

The first thing to do is what is the Vedic theorem:

Vieta's Theorem (Vieta's theorem) is an important theorem in algebra that describes the relationship between the roots and coefficients of polynomials. Specifically, for an nth degree polynomial:

p(x) =aₙxⁿ +aₙ₋₁xⁿ⁻¹a₁x + a₀

where a, a a, a are the coefficients of the polynomial, and x, x, x are the roots of the polynomial. The Vedadine Stuffy Stove Theory gives the relationship between roots and coefficients:

x +x +x =a Congratulations a

x₁x₂ +x₁x₃ +xₙ₋₁xₙ =aₙ₋₂aₙ

x₁x₂..xₙ =1)ⁿa₀/aₙ

In other words, Veda's theorem tells us that the sum of the roots of a polynomial is equal to the inverse of the ratio of the coefficients a to a, and the product of the roots is equal to the nth power of the inverse of the ratio of the coefficients a to a.

Vedic theorem has a wide range of applications in algebra, especially in the solution of polynomial equations and the derivation of the relationship between roots and coefficients.

The first Zen cover Zheng 2 Veda theorem to find the root:

Vedica's theorem can be used to solve the problem of the relationship between the roots and coefficients of polynomial equations. Specifically, it can be used for the following purposes:

Solving the Root of a Polynomial Equation: With Vedica's theorem, we can calculate the root of a polynomial equation based on the coefficients of a polynomial. By solving the root, we can find the analytic or numerical solution of the polynomial equation.

Derive the coefficients of polynomial equations: Knowing the root of polynomial equations, we can use Veda's theorem to inversely deduce the coefficients of polynomial equations. This is useful in practical problems, such as fitting a polynomial function based on known data points.

Determine the properties of polynomial equations: Through Vedica's theorem, we can get the relationship between the sum of the roots, the product of the roots, etc., and the coefficients of the polynomial equations. These relations can help us determine the properties of polynomial equations, such as whether the roots of polynomial equations are real numbers, whether the sum of the roots of polynomial equations is zero, and so on.

In conclusion, Vedic theorem has a wide range of applications in algebra that can help us understand and solve problems related to polynomial equations.

The formula for finding the root is:

ax²+bx+c=0,a≠0

x1=[-b- (b -4ac)] 2a)x2=[-b+ (b -4ac)] 2a) Vedadine repentance is:

x1+x2=-b/a

x1*x2=c/a

Theorem significanceVedic theorem has a unique role in finding the symmetry function of the root, discussing the sign of the root of a quadratic equation, solving the system of symmetric equations, and solving some problems about quadratic curves.

The discriminant formula for the root of the unary quadratic equation is (a, b, and c are the quadratic coefficients, the primary coefficients, and the constant terms of the unary quadratic equations, respectively). The relationship between Vedic theorem and the discriminant formula of the root is even more inseparable.

The discriminant of the root is a sufficient and necessary condition for determining whether an equation has a real root, and Veda's theorem explains the relationship between roots and coefficients. Regardless of whether the equation has a real root or not, the relationship between the roots and the coefficients of a quadratic equation with real coefficients fits Vedica's theorem. The combination of discriminant formula and Vedic theorem can more effectively explain and determine the condition and characteristics of the root of a quadratic equation.

If the equation for x x 2+mx+m-1=0 has a positive root and a negative root in Kaitan, and the absolute value of the negative root is larger, find the range of the value of the real number m.

One positive root and one negative root.

So discriminant 0

m^2-4*1*(m-1)>0 .(1)

By the Vedic theorem there is:

The product of two roots = m-1

In the unary quadratic equation ax 2+bx+c=0 (a≠0 and =b 2-4ac 0), let the two roots be x1 and x2 Vedic theorem:

Then x1+x2= -b a x1*x2=c a>0, then x1 and x2 have the same sign, both positive or negative.

If -b a >0, then x1 and x2 are positive.

If -b a <0, then x1 and x2 are negative.

0, then x1 and x2 different signs, and then judge according to the question conditions.

Judge the root of an equation using Veda's theorem:

If b 2-4ac>0 then the equation has two unequal real roots, if b 2-4ac=0 then the equation has two equal real roots, and if b 2-4ac 0 then the equation has real roots.

If b 2-4ac<0 then the equation has no real solution.

Taking the unary quadratic equation as an example, the discriminant formula for the root of the unary quadratic equation ax 2+bx+c=0(a≠0) δ=b 2-4ac, and Vedda's theorem explains the relationship between the roots and the coefficients in the equation.

x1+x2=-b/a

x1*x2=c/a

However, Veda's theorem does not explain the case of the roots of equations, and in order to know whether the original equation (in the range of real numbers) has roots, no roots, and how many roots there are, it is necessary to use the root discriminant.

Most of the time, the role of the discriminant formula will be replaced by the Vedic theorem, but there are also problems that will set the role of the discriminant formula is stronger, so for the sake of rigor, the discriminant formula must be used before using the Vedic theorem. However, if the product of the two roots is less than zero, the discriminant formula does not need to be considered.

Vedic theorem. x1+x2=-b/a

x1x2=c/a

Discriminant formulas of equations.

b squared -4ac

The equation has two unequal real roots.

The equation has two equal real roots.

Equations have no real roots.

Vedic theorem x1+x2=-b a x1x2=c a discriminant of the equation δ = b squared -4ac

The 0 equation has two unequal real roots.

The 0 equation has two equal real roots.

0 equations have no real roots.

The two roots of the unary quadratic equation ax 2+bx+c=0 are x1 and x2, then there are x1+x2=-b a, x1*x2=c a, the discriminant formula of the root of the equation: by calculating the value of b 2-4ac, when it is greater than 0, the equation has two unequal real roots, when it is equal to 0, the equation has two equal real roots, and when it is less than 0, the equation has no real roots.

In the unary quadratic equation ax 2+bx+c=0 δ 0, the two x1 and x2 have the following relationship: x1+ x2=-b a, x1·x2=c a

b^2－4ac．