If ` f(x) = ax^(2) + bc + c ` , where ` a ne 0, b ,c in ` R , then which of
the following conditions implies that f(x) has real roots?

Options

A. a+ b + c = 0
B. a and c are of opposite signs
C. ` 4ac - b^(2) lt 0 `
D. a and b are of opposite signs

Answer

1,2,3,

Explanation

(1) If ` f(1) = 0 rArr a + b + c = 0`
so, roots are real.
(2) ` D = b^(2) - 4ac`
If ` ac lt 0 rArr b^(2) - 4ac gt 0 `
(3) ` 4ac - b^(2) lt 0 rArr b^(2) - 4ac gt 0 `
So, roota are real .
This is not the sufficients condition