If the zeroes of the quadratic polynomial ax2 + bx + c, c≠0 are equal, then . . .

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

Doubt by Zoha

Solution :

We know, when zeroes are equal then Discriminate (D)=0
[From the Chapter - 4, Quadratic Equations]

Zeroes are equal (Given)
D = 0 
b²-4ac=0
b²=4ac
The square of a real number can't be negative. 
Hence, 4ac must be positive which is only possible when 'a' and 'c' both have either -ve sign or +ve sign. 

Hence, c) c and a have the same sign, is the right option.