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If f(x) = ax^(2) + bx + c , where a ...

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

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

Text Solution

Verified by Experts

The correct Answer is:
1,2,3,
(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
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