Junior high school 9th grade one dimensional quadratic equation math problem

There are x people to go, obviously x > 25, (because if x25, the cost is 25,000 yuan, and the actual cost is 27,000 yuan, which does not match.) )

So the cost per person should be 1000-20 (x-25) = 1500-20x yuan, so it is derived from the title.

1500-20x)*x=27000, so -20x 2+1500x-27000=0, so 2x 2-150x+2700=0, so (x-30)(2x-90)=0, so x=30 or x=45, when x=30, 1500-20x=900>700 conforms to the topic;

When x=45, 1500-20x=600<700, it doesn't fit the topic, so there are 30 people to go.

1000 25 25000 27000.

The number of people is more than 25.

Let's say there are x people beyond 25 people.

25+x）（1000-20x）＝27000 25000-27000-500x+1000x-20x·x＝0

Solution x1 , x2

Then round off one of them according to not less than 700 yuan.

The total number of people is 25+x

I'm sorry.,Because I'm in a hurry, I can't help you figure it out.。。 Trouble yourself.

As follows; Known; About the unary quadratic equation mx 2; -（3m 2)x 2m 2=0(m

1. The previous one in the equation, etc.

If it is, because it is a right triangle, there is a 2+b 2=c 2 that is, (a+b) 2-2ab=c 2, according to Veda's theorem, a+b=7, a*b=c+7, so 49-2(c+7)=c2 is solved to get c=7 or -5 (not in line with the topic, rounded), and the area of the triangle a*b 2=(c+7) 2=14 2=7

2. The equation can be reduced to x 2-5x+6-p =0, δ 5) 2-4(6-p)=1+p >0, so the equation has two unequal real roots.

（1）3x²-6x+1=0

quadratic term coefficient 3; The coefficient of the primary term is -6; Constant term 1

2）4x²+5x-81=0

quadratic term coefficient 4; coefficient of the primary term 5; Constant term -81

3）x²+5x=0

quadratic term coefficient 1; coefficient of the primary term 5; Constant term 0

4）2(x-1)²=0

x-1)²=0

x²-2x+1=0

quadratic term coefficient 1; The coefficient of the primary term is -2; Constant term 1

5）x²+5x=5x-10

x²+10=0

quadratic term coefficient 1; The coefficient of the primary term is 0; Constant term 10

6）3x²+x-2 = 2x²-x

x²+2x-2=0

quadratic term coefficient 1; The coefficient of the primary term is -2; Constant term -2

1. Because x1x2=1, so m 2=1, so m = 22, from the judgment of the rise and perturbation equation (-2) -4*1*k is greater than or equal to 0: k is less than or equal to 13, because a is a root of the unary quadratic equation x 2-3x+m=0, so a 2-3a+m=0, then m=-(a 2-3a).

Since -a is a root of x 2+3x-m=0, then a 2-3a-m=0, then m=a 2-3a

So -(a 2-3a) = a 2-3a

So a=0 or a=3

4. Let x1·x2=m, x1+x2=n, then the original formula can be turned into.

m+n+2=0

m-2n+5=0

The solution: m=-3, n=1

Thus x1·x2=-3, quietly x1+x2=1

Therefore, the equation for Qixiaoling is x 2-x-3 = 0

Solution: Set the sales price to be X yuan.

180-(x-52)*10]*(x-40)=2000 solution: x1=50 x2=60

Because x>52 so x=60

At this time, the sales volume is 180-(60-52)*10=100 A: 100 pcs. The pricing is $60.

Set the sales price (up from 52 yuan) by X yuan.

The profit is (52+x-40) yuan, and the sales volume is (180-10x).

52+x-40)*(180-10x)=2000x1=-2(rounding).

x2=8 is priced at 60 yuan, and 100 should be purchased.

The set price is increased by X yuan.

52+x-40)*(180-10*x)=2000 to get x=8, x=-2 (rounded).

That is, the pricing is 52+x=52+8=60 (yuan), so the purchase is 180-10*x=100 (pcs).

Answer: 100 pieces should be purchased; The pricing is $60.

Let the purchase be x and the pricing be y

xy-x*40=2000

180-(y-52)*10=x

Bring in x=700-10y.

y2-110y+3000=0

Get y=50 or 60

Because the sales price is 52 yuan, the ** of 50 yuan will be rounded.

So y=60 yuan.

then we get x=100.

Therefore, 100 should be purchased, and the price is 60 yuan.

Set price x yuan.

x-40)*[180-10*(x-52)]=2000x=60

The incoming stock is 180-10 * (60-52) = 100 pcs.

Solution: If the average annual growth rate is x (the same growth rate for two years), it will increase to 144 (1+x) million units in the first year, and 144 (1+x) (1+x) million units in the second year.

144(1+x)(1+x)=169

1+x)²=169/144

x+1>0

x+1=13/12

x=1/12

This is therefore an average annual growth of 1 12

Let the growth rate be x, then 144*(1+x) 2=169 solution x=1 12=

Solution: Let the average annual approximate growth rate be x

144（1+x）²=169

The solution yields x1 = 1 12, x2 = -25 12

x=-25 12 is not on topic.

x=1/12

A: The growth rate is x

The test is the Vedic theorem.

x1+x2=-p/1=-p

x1*x2=q/1=q

Proof =p -4q (discriminant, right?) ）

p+2q)*(p-2q）

x1=[-p+（p+2q)*(p-2q)]/2,x2=[-p-(p+2q)*(p-2q)]/2

x1+x2=[-p+（p+2q)*(p-2q)]/2+[-p-(p+2q)*(p-2q)]/2

2p/2-px1*x2=[-p+（p+2q)*(p-2q)]/2*[-p-(p+2q)*(p-2q)]/2

p-(p+2q)²（p-2q)²

Q (If you don't understand it, come to me).

If the unary quadratic equation x +px+q=0 (p,q is the coefficient) has two x,x, you say x,x, no difference.

I'll just swap the two for x and y

Relation: x+y=-p xy=q

Proof of it: Fix it yourself.

(m-2) x +(2m+1)x+1=0 with two unequal real roots, then m-2≠0

Discriminant formula =(2m+1) -4(m-2) 0 is simplified to 20m-15 0

Solution m≠2

Solution m 3 4

The value range of m is m 3 4 and m ≠ 2

1. A is the root of the equation about x, bring x=a into the equation to get a 2+ab+a=0, and mention the common factor a(a+b+1)=0, if a is not equal to 0, then the factor a+b+1=0, then a+b=-1.

2. Bring x=2+1 into the equation to get (2+1) 2-k( 2+1)+1=0, and sort out the equation to get k=2 2.

3. The original equation is sorted out according to the decreasing power to obtain (1-2a) x 2 + (a 2-a-1) x = 0, the quadratic coefficient is 1-2a, and the primary term coefficient is a 2-a-1.

1.Bring A into it to get a 2+ab+a = 0, and you can get it by going to A on both sides. a+b=-1

2.Because the root number 2+1 is brought into the original equation, k can be obtained as 2*root number 2

3.If a=1 2, it is not. It's not the same, it's it. The coefficient of the quadratic term is: (1-2a), and the coefficient of the primary term is: a 2 -1

1.Because a is the root of the equation, the square of a + ab + a = 0 is a (a + b + 1) = 0 and because a is not equal to 0, a + b + 1 = 0 is a + b = -1.

2.Bring in: 2+1+2 times the root number, 2-k times the root number, 2-k+1=0, that is, k=2 times the root number 2

3.If a=1 2 is not, otherwise, the quadratic coefficient is 1-2a, and the primary term coefficient is -(the square of a + a).

(1) Solution: From the meaning of the question, it can be obtained: a 2 + ab + a = 0 so a + b + a = 0 so a + b = a so b = 0

The original formula gives x 2+a=0, i.e. a 2+a=0, because a is not equal to 0, so a= - 1, so a+b=-1

2) From the meaning of the title: 2+1-k root number 2+1+1=0 so -k* follows 2+1=-4 so k=4 (root number 2+1) numerator denominator multiplied by root number 2-1 at the same time to get k=4 3

3) Is a multiplied by the number in parentheses or ax multiplied by the ???number in parentheses?