If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then
(A) c and a have opposite signs (B) c and b have opposite signs
(C) c and a have the same sign (D) c and b have the same sign

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Solution

Given that, the zeroes of the quadratic polynomial ax² + bx + c , c ≠ 0 are equal
⇒ Value of discriminant (D) has to be zero
i.e. b² – 4ac = 0
⇒ b² = 4ac
Since L.H.S. (b²) can never be negative
⇒ R.H.S. also can never be negative.
∴ a and c must have same sign
[∴ if a and c have opposite sign, then a × c will be negative which is not possible.]

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