Question

Let P(x) be a quadratic polynomial P(3) = 8 and P(–3) = –10. Then the coefficient of x in P(x) is
A) 4 B) 5 C) 3 D) 6

Answer 1

Let the Quadratic Polynomial P(x) be : ax² + bx + c

Given : P(3) = 8

⇒ a(3)² + b(3) + c = 8

⇒ 9a + 3b + c = 8 --------------------- [1]

Given : P(-3) = -10

⇒ a(-3)² + b(-3) + c = -10

⇒ 9a - 3b + c = -10 -------------------- [2]

Subtracting Equation [2] from Equation [1], We get :

⇒ (9a + 3b + c) - (9a - 3b + c) = 8 + 10

⇒ 9a + 3b + c - 9a + 3b - c = 18

⇒ 6b = 18

⇒ b = 3

⇒ The Coefficient of x in P(x) is 3