Question

If $\lambda$ has two rational factors, then the value of m will be.

• A. $\alpha^{2} + \beta^{2}$
• B. $f(x) = x^{2} + 4x + 1$
• C. $f(x) > 0$
• D. 6, 2

Answer 1

Answer: (C)

$f(x) > 0$

Answer 2

Given expression $\frac{2b}{ac}$ can be written as $\frac{2b}{\sqrt{ac}}$

But factors are rational, so $7 + 5i$ is a perfect square.

Now $x^{2} + 14x + 74 = 0$

⇒$x^{2} - 14x - 74 = 0$⇒ $x^{2} + 14x - 74 = 0$

Hence $\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}$ {as it is perfect square}

⇒ $\frac{p^{2} + q^{2}}{2}$.

Now taking (–) sign, we get $\frac{(p^{2} + q^{2})}{2}$.