The polynomial f(x) = x 4 + ax 3 + bx 2 + cx + d has real c…

Maths Quadratic Equations Relation Between Roots and Coefficients - Quadratic Equations Single Correct MCQ

Published on: August 14, 2026

The polynomial f(x) = x 4 + ax 3 + bx 2 + cx + d has real coefficients and f (2i) = f(2 + i) = 0. The value of (a + b + c + d) equals to-

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The correct answer is:

If a polynomial has real coefficients, then roots occur in

complex conjugate and roots are 2i, –2i, 2 + i, 2 – i.

Hence, f(x) = (x + 2i)(x – 2i)(x – 2 – i)(x – 2 + i)

f(1) = (1 + 2i)(1 – 2i)(1 – 2 – i)(1 – 2 + i)

f(1) = 5 × 2 = 10

Also, f(1) = 1 + a + b + c + d

∴ 1 + a + b + c + d = 10

⇒ a + b + c + d = 9.

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