-
Anonymous users2024-02-11The equation is 2x 2 + 4x + k-1 = 0
Solution: 1) Discriminant = 16-8*(k-1) 0
k 3 so k = 1 or k = 2 or k = 3
2) Test to get k=3
y=2x^2+4x+2
Translate to y=2x 2+4x-6
Under the condition of (2), the quadratic function is y=2x 2+4x+2, and the analytic formula of the image obtained by translating the image y=2x 2+4x+2 downwards by 8 units: y=2x 2+4x-6;
Let the quadratic function y=2x 2+4x-6 intersect the x-axis at a and b, then we have: a(-3,0),b(1,0).
When the straight line y= 1 2x+b passes through point a, b= 3 2;
When the line y= 1 2x+b passes through point b, b=- 1 2 is obtained
As can be seen from the image, when the value range of b is -1 2 b 3 2, there are 2 intersection points.
The value of b can range from 3 2 b<273 32, and there are 4 intersecting points.
The discriminant formula =0 of the quadratic trinomial formula 4x 2+9x+2b-12=0 can be solved from the discriminant formula =0 of 2x 2+4x-6=-(1 2x+b) and the b value = 273 32].
The value range of b is 273 32 b, and there are 2 intersections at the intersection.
-
Anonymous users2024-02-10It is known that the unary quadratic equation 2x 2+4x+k-1=0 about x has a real root, and k is a positive integer. （1）2x^2+4x+k-1=0 16-8（k-1）》=0 k=1，2，3。 y=2x^2+4x+k
-
Anonymous users2024-02-092**Equation 4 x 2 + 4 kx + k 2 = 0
4*(-2)^2+4k(-2)+k^2=0k^2-8k+16=0
k=4 (equal root).
4x^2+4*4x+16=0
x^2+4x+4=0
The other root = 4 1 (2) = -2
-
Anonymous users2024-02-081) δ=36+4k 0, the equation has two unequal real roots.
2) x1 and x2 are the two real roots of the equation.
From Veda's theorem:
x1+x2=6, and x1+2x2=14
Solving the system of equations yields x1=-2, x2=8.
-
Anonymous users2024-02-071. Prov: =36-4 1 (-k )=36+4k 0 There are two real roots that do not want to wait.
2. Solution: the relationship between the root and the coefficient, x1+x2=6
x1+2x2=14
x1=-2 x2=8
-
Anonymous users2024-02-06Original question: It is known that the unary quadratic equation 2x 2+4x+k-1=0 about x has a real root, and k is a positive integer. (1) Find the value of k (2) When this equation has two non-zero integer roots, shift the image of the quadratic function about x y=2x 2+4x+k-1 down by 8 units, find the analytical formula of the translated image (3) under the condition of (2), fold the part of the translated image below the x-axis along the x-axis, and keep the rest of the image unchanged to obtain a new image.
When the straight line y=1 2x+b(b solution:1) discriminant = 16-8*(k-1) 0
k 3 so k = 1 or k = 2 or k = 3
2) Test to get k=3
y=2x^2+4x+2
Translate to y=2x 2+4x-6
Under the condition of (2), the quadratic function is y=2x 2+4x+2, and the analytic formula of the image obtained by translating the image y=2x 2+4x+2 downwards by 8 units: y=2x 2+4x-6;
Let the quadratic function y=2x 2+4x-6 intersect the x-axis at a and b, then we have: a(-3,0),b(1,0).
When the straight line y= 1 2x+b passes through point a, b= 3 2;
When the line y= 1 2x+b passes through point b, b=- 1 2 is obtained
As can be seen from the image, when the value range of b is -1 2 b 3 2, there are 2 intersection points.
The value of b can range from 3 2 b<273 32, and there are 4 intersecting points.
The discriminant formula =0 of the quadratic trinomial formula 4x 2+9x+2b-12=0 can be solved from the discriminant formula =0 of 2x 2+4x-6=-(1 2x+b) and the b value = 273 32].
The value range of b is 273 32 b, and there are 2 intersections at the intersection.
-
Anonymous users2024-02-05Under the condition of (2), the quadratic function is y=2x 2+4x+2, and the analytic formula of the image obtained by translating the image y=2x 2+4x+2 downwards by 8 units: y=2x 2+4x-6;
Let the quadratic function y=2x 2+4x-6 intersect the x-axis at a and b, then we have: a(-3,0),b(1,0).
When the straight line y= 1 2x+b passes through point a, b= 3 2;
When the straight line y= 1 2x+b passes through point b, b=- 1 2 can be seen from the image, when the value range of b is -1 2 b 3 2, the value range of the intersection of 2 intersection points b is 3 2 b<273 32, and there are 4 intersection points [the discriminant formula of the quadratic trinomial formula 4x 2+9x+2b-12=0 obtained from 2x 2+4x-6=-( 1 2x+b) can be solved and the b value = 273 32].
The value range of b is 273 32 b, and there are 2 intersections at the intersection.
I hope it can help you, give it approval, flowers, and the best.
-
Anonymous users2024-02-041): is a quadratic equation k≠0 (2): x1+x2=-2 k, x1,x2 is an integer, -2 k 2 x1x2=(2-k) k k takes -2,-1,1,2(3):
x1-x2|=2, (x1-x2) =x1 +x2 -2x1x2=4, (x1+x2) =x1 +x2 +2x1x2=4 k and x1x2=(2-k) k, 4 k -4(2-k) k=4, 1 k -(2-k) k=1, k=1 2
-
Anonymous users2024-02-03Proof: Because =k 2-4(k-2)=k 2-4k+8=(k-2) 2+4>0
So >0, so there are two unequal real roots.
x1=(k - k-2)^2+4)/2, x2=(k + k-2)^2+4)/2
Because x1 * x2 = (k2 - k2 + 4k - 8) 4=k-2=6
So k = 8 (x1 + x2) *2 = 16
So the circumference is 16
1. Solution: From the meaning of the question: two equal real roots, that is, =0=k -4 1 1=0 k =4 k= 2Answer: When k= 2, there are two equal real roots. >>>More
Solution: In the form of an +bn + c, it can be matched into a(n+b 2a) +4ac-b ) 4a, and the square term in front can determine n, such as a<0, a(n+b 2a) has a maximum value of 0, (if and only if n=-b 2a, etc.), so that the n value can be determined, and then the whole can be determined.
Divide by 3 to get x 2+2x-4 3=0
Recipe x 2+2x+1-1-4 3=0 x+1) 2-7 3=0 Then move the root to get two. >>>More
private sub command1_click()dim a, b, c, x1, x2, d as singlea = val( >>>More
By the first equation, there is:
x1+x2=-p...1) >>>More