Question

If $\alpha^{2} + \beta^{2} + \gamma^{2}$ and $\frac{15}{4}$ are the roots of the equation $\frac{15}{4}$,then the equation whose roots are $\frac{9}{4}$ and $pqx^{2} - (p + q)^{2}x + (p + q)^{2} = 0$ is.

• A. $\left\{ \frac{p}{q},\frac{q}{p} \right\}$
• B. $\left\{ pq,\frac{p}{q} \right\}$
• C. $\left\{ \frac{q}{p},pq \right\}$
• D. $\left\{ \frac{p + q}{p},\frac{p + q}{q} \right\}$

Answer 1

Answer: (A)

$\left\{ \frac{p}{q},\frac{q}{p} \right\}$

Answer 2

$\mathbf{b}^{\mathbf{2}}\mathbf{+ 3ac = 0}$ and $3x^{2} - 20x + 17 = 0$

$\mathbf{3}\mathbf{x}^{\mathbf{2}}\mathbf{+ 20x}\mathbf{-}\mathbf{17 = 0}$

Hence required equation

$17x^{2} - 20x + 3 = 0$

⇒$17x^{2} + 20x + 3 = 0$⇒ $x^{2} + 2x + 4 = 0,$