Question

The difference of the roots of $2y^2-ky+16=0$ is 1/3 Find k

• A. $\pm \frac{30}{3}$
• B. $\pm \frac{32}{3}$
• C. $\pm \frac{34}{3}$
• D. $\pm \frac{38}{3}$

Answer 1

Answer: (C)

$\pm \frac{34}{3}$

$a{y}^2+by+c=0$ where $\alpha ,\beta$ are the roots of the equation

$\alpha ,\beta =\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

the given equation is $2y^2-ky+16=0$

now we have to find $\alpha -\beta =?$

$\alpha -\beta =\left(\frac{-b+\sqrt{b^2-4ac}}{2a}\right)-\left(\frac{-b-\sqrt{b^2-4ac}}{2a}\right)\alpha -\beta =\frac{2\sqrt{b^2-4ac}}{2a}$

after using this

$\alpha -\beta =\frac{2\sqrt{k^2-4\times 2\times 16}}{2\times 2}=\frac{1}{3}\sqrt{k^2-128}=\frac{2}{3}k=\pm \frac{34}{3}$