Question

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2-12x+35=0$, then find the value of $2\left(\begin{array}{c}\frac{\alpha }{\beta }+\frac{\beta }{\alpha }\end{array}\right):$

• A. $\frac{74}{35}$
• B. $\frac{148}{35}$
• C. $\frac{12}{35}$
• D. $\frac{34}{35}$

Answer 1

The correct option is B $\frac{148}{35}$

Let us solve the given quadratic equation $x^2-12x+35=0$

$⟹$ $x^2-7x-5x+35=0$

$⟹(x-7)(x-5)=0$

$⟹x-7=0$ or $x-5=0$

$⟹x=7$ or $x=5$

Thus, $7,$ are roots of the given equation.

Let $\alpha =7$ and $\beta =5$

$\therefore 2(\frac{\alpha }{\beta }+\frac{\beta }{\alpha })=2(\frac{7}{5}+\frac{5}{7})=2\left(\frac{74}{35}\right)=\frac{148}{35}$

Hence, option B is correct.