Question

Given that 2 is a root of the equation 3x² – p(x + 1) = 0 and that the equation px² – qx + 9 = 0 has equal roots, find the values of p and q.

Answer 1

Since 2 is a root of the equation 3x² – p(x + 1) = 0

⇒ 3(2)² – p(2 + 1) = 0

⇒ 3 × 4 – 3p = 0

⇒ 12 – 3p = 0

⇒ 3p = 12

⇒ p = 4

Now the other equation become 4x² – qx + 9 = 0

Here a = 4, b = – q and c = 9

Since then root are equal we have

b² – 4ac = 0

⇒ (– q)² – 4 × 4 × 9 = 0

⇒ q² – 144 = 0

⇒ q² = 144

⇒ q = 12

Hence, p = 4 and q = 12