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Quantitative Aptitude

Solving Inequalities

Question 11 ....

Question

Question 11.
$(x^{2} + 1)^{2} - x^{2} = 0$ has:

(a) four real roots

(b) two real roots

(c) no real roots

(d) one real roots

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Solution

Option (C)
Given, $(x^{2} + 1)^{2} - x^{2} = 0$
$\Rightarrow (x^{2} + 1)^{2} = x^{2}$
Square root on both sides. We get,
$x^{2} + 1 = x o r x^{2} + 1 = - x$
$\Rightarrow x^{2} - x + 1 = 0 o r x^{2} + x + 1 = 0$
discriminant for the above equations will be;
1-4 = -3 <0 or 1-4=-3 <0
Hence, $(x^{2} + 1)^{2} - x^{2} = 0$ has no real roots.

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