Question

If the polynomial f(x) = x2 + (p2 + q)x + q - 9 is negative of the polynomial
g(x) = - x2 - 5px +q-3 for every x € R, then
(A) p = 2, q = 6 (B) p = 6,9 = 2 (C) p = 3, q = 6 (D) p = 6,4 = 3

Answer 1

Answer:

If in equation ax

2

+bx+c=0 the two roots are equal

Then b

2

−4ac=0

In equation px

2

−2

5

px+15=0

a=p,b=−2

5

p and c=15

Then b

2

−4ac=0

⇒(−2

5

p)

2

−4×p×15=0

⇒20p

2

−60p=0

⇒20p(p−3)=0

So when p−3=0⇒p=3

p



=0 as it makes coefficient of x

2

=0

Hence, p=3