One or more options can be correct:

The condition for the roots of the quadratic equation f(x)= a $x^{2}$ +bx+c to be less than a real value x₀ is/are

f(x₀) > 0

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f(x₀) < 0

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D ≥ 0

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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 = $m^{2}$ - 1

Observe that (i) f(x₀) > 0

(ii) x₀ > $\frac{(- b)}{2 a}$

Also for real roots to exist (iii) $b^{2}$ ≥ 4ac

Hence, A, C, D are right options.

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