if the zeroes of the quadratic polynomial p(x)=ax2+bx+c, a is not = to 0, are equal then,

A) a and c have opposite signs

B) b and c have opposite signs

C) a and c have same signs

D) b and c have same signs

explain plz.

ans- option C

Given that the roots of ax^2 +bx+c=0 are equal

So, its discriminant D=0

b^2-4ac=0

Since b^2 is always positive for any value of b, for getting b^2-4ac =0, the value 4ac must be positive. 

(If 4ac is negative then D= b^2-4ac = (positive)-(-negative)=positive+positive will leave a positive quantity, but here D=0)

So, 4ac ≥0

ac≥0

This is possible only when both 'a' and 'c' are positive.

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