Correct Answer - C
The zeroes of the given quadratic polynomial `ax^(2)+bx +c, c ne 0` are equal. If coefficient of `x^(2)` and constant term have the same sign i.e., c and a have the same sign. While b i.e., coefficient of x can be positive/negative but not zero.
e.g., (i) `x^(2)+4x +4 = 0 " "(ii) x^(2)-4x +4 = 0`
`rArr (x+2)^(2)=0 " "rArr (x-2)^(2)=0`
`rArr x =- 2, -2 " "rARr x = 2,2`
Alternative Method
Given that, the zeroes of the quadratic polynomial `ax^(2) +bx +c`, where `ne 0`, are equal i.e., discrinminant `(D) = 6`
`rArr b^(2)-4ac = 0`
`rArr b^(2) = 4ac`
`rArr ac = (b^(2))/(4)`
`rArr ac gt 0`
Which is only possible when a and c have the same signs.
