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.