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Question

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

Let the given quadratic polynomial be f(x) = ax2+bx+c.
Suppose α and β be the zeroes of the given polynomial.
Since α and β are equal so they will have the same sign i.e. either both are positive or both are negative.
So, αβ>0
But, αβ=ca
ca>0, which is possible only when both have same sign
Hence, the correct answer is option C.

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