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Question:

What is the other root of f(x) = 0?

Explanation:

∵ 3 is a root of f(x) = 0,

∴ 9a + 3b + c = 0           …(i)

Also,

f(5) = −3f(2)

∴ 25a + 5b + c = −3(4a + 2b + c)

∴ 37a + 11b + 4c = 0       …(ii)

On solving equations (i) and (ii), we get,

a – b = 0

∴ a = b

We know that sum of the roots of a quadratic equation (ax² + bx + c = 0) is –b/a

∴ 3 + other root = −1

∴ Other root = −4

Hence, option (b).