Question

If px2+3x+q=0 has two roots x=1 and x= -2, find p-q.​

Answer 1

Answer :

p - q = 9

Step-by-step explanation :

Given quadratic equation,

px² + 3x + q = 0

It has two roots, x = 1 and x = -2,

Put x = 1,

p(1)² + 3(1) + q = 0

p(1) + 3 + q = 0

p + 3 + q = 0

$\boxed{p+q=-3}$

=> q = -3-p

Put x = -1,

p(-2)² + 3(-2) + q = 0

p(4) - 6 + q = 0

4p - 6 + q = 0

$\boxed{4p+q=6}$

Substitute the value of q,

4p + (-3-p) = 6

4p - 3 - p = 6

 3p - 3 = 6

  3p = 6+3

  3p = 9

  p = 9/3

  p = 3

=> q = -3-p

    q = -3-3

    q = -6

⇒ p-q = 3 - (-6)

          = 3 + 6

          = 9