Question

If `(2)/(3)` and – 3 are the roots of the equation px²+ 7x + q = 0, find the values of p and q.

Answer 1

`(2)/(3)`  and – 3 are the roots of the equation px²+ 7x + q = 0
Substituting the value of x =  and – 3 respectively, we get

`"p"(2/3)^2 + 7(2/3) + "q"` = 0

⇒ `(4)/(9)"p" + (14)/(3) + "q"` = 0

⇒ 4p + 42 + 9q = 0
⇒ 4p + 9q = -42           ...(i)
and
p(-3)² + 7(-3) + q = 0
9p - 21 + q = 0
⇒ 9p + q = 21              ...(ii)
q = 21 - 9p
Substituting the value of q in (i)
4p + 9(21 - 9p) = -42
4p + 189 - 81p = -42
-77p = -42 - 189 = -231

p = `(-231)/(-77)` = 3

∴ q
= 21 - 9 x 3
= 21 - 27
= -6
∴ p = 3, q = -6.