Question

If f(x) = 4x² + 3x – 7 and a is a common root of equations

x² – 3x + 2 = 0 and x² + 2x – 3 = 0, then f(a) =

• A. 3
• B. 2
• C. 1
• D. 0

Answer 1

Answer: (D)

0

Answer 2

a is a common root, $\frac{\begin{aligned} & \alpha^{2}–3\alpha + 2 = 0 \\ & \alpha^{2} + 2\alpha –3 = \alpha \end{aligned}}{\alpha = 1}$ so,

f(a) = f(1) = 4(1)² + 3(1) – 7 = 0