Question

If -1 and 3 Are the Roots of X2+Px+Q=0 Then Find the Values of P and Q

plz answer and also pls sub to DTS roblox on ut ube

Answer 1

Answer:

If -1 and 3 are the roots of x²+px+q=0, what is the value of p and q?

Since -1 and 3 are the roots of the gien equation ,it will satisfy the equation .

Putting X= -1 in given equation ,we get

(-1)^2+p(-1)+q=0

1-p+q=0

p=q+1 ------ equation (1)

Again putting X= 3 in given equation, we get

(3)^2+p.3+q=0

9+3p+q=0

Putting p=q+1 from equation (1)

9+3(q+1)+q=0

9+3q+3+q=0

12+4q=0

4q= -12

q= -12/4= -3

From equation (1)

p=q+1= -3+1= -2

Hence p= -2 and q= -3

Another method,

Since -1 and 3 are the roots of given equation.

Therefore x^2+px+q=(x+1) (x-3)

x^2+px+q = x^2-3x+x-3

x^2+px+q = x^2-2x-3

On comparing we get p= -2 and q= -3

Hence p= -2 and q= -3

Hope it will help you. Please do tell me which method you prefer. Thanks.

We can solve it with Sum-and-Product Method.

If we have an equation of the form

ax2+bx+c=0

The sum of the roots is

x1+x2=−ba

And the product is

x1⋅x2=ca

In your equation, we have

a=1

b=p

c=q

So, the sum of the roots is

−1+3=−p1

2=−p

−2=p

p=−2

The product of the roots is

(−1)⋅(3)=q1

−3=q

q=−3

So, we have p=−2 and q=−3 .