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Question

One or more options can be correct:

The condition for the roots of the quadratic equation f(x)= a x2+bx+c to be less than a real value x0 is/are


A

f(x0) > 0

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B

f(x0) < 0

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C

D 0

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D

x0 >

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Solution

The correct options are
A

f(x0) > 0


C

D 0


D

x0 >


Conditions for both roots to be less than a real value x0, can be visualized through graph

Here, a = 1 (> 0), b = -2m, c = m2 - 1

Observe that (i) f(x0) > 0

(ii) x0 > (b)2a

Also for real roots to exist (iii) b2 4ac

Hence, A, C, D are right options.


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