Question

The quadratic equation whose one root is $x^{2} - 5|x| + 6 = 0$ will be.

• A. $(m^{2} + 1)x^{2} + 2amx + a^{2} - b^{2} = 0$
• B. $a^{2} + b^{2}(m^{2} + 1) = 0$
• C. $b^{2} + a^{2}(m^{2} + 1) = 0$
• D. $a^{2} - b^{2}(m^{2} + 1) = 0$

Answer 1

Answer: (A)

$(m^{2} + 1)x^{2} + 2amx + a^{2} - b^{2} = 0$

Answer 2

Let $S = ax + (1 - a)x^{2}\ \forall a \in (0,\infty)$ and $S = ax + (1 - a)x^{2}\ \forall a \in R$

Sum of roots $S = ax + (1 - a)x^{2}\ \forall a \in (0,2)$ and product of roots $\alpha$

Thus required equation is $\beta$.