IF the roots of the equation `ax ^2 +bx + c=0` are real and distinct , then

Options

A. both roots are greater than `(-b)/(2a)`
B. both roots are less than `(-b)/(2a)`
C. one of the roots exceeds `(-1)/(2a)`
D. none of these

Answer

C

Explanation

The roots of the given equation are
`alpha=(-b-sqrt(b^(2)-4ac))/(2a)and beta=(-b+sqrt(b^(2)-4ac))/(2a)`
Since `alpha, beta` are real and distinct, therefore `b^(2) - 4ac gt 0`.
It is evident from Fig. 1 that `beta lt - (b)/(2a) lt alpha`.

So, one root is less than `-(b)/(2a)` and other exceeds `-(b)/(2a)`.