Question

If $\propto$ and $\beta$ are roots of ${ax}^2-4x+c=0$ then what is length of hypotenuse of right angled triangle whose perpendicular sides are $\propto$ and $\beta$?

• A. $\frac{\sqrt{16+2ca}}{a}$
• B. $\frac{\sqrt{16-2ac}}{a}$
• C. $\sqrt{\frac{16-2ac}{a}}$
• D. $\sqrt{\frac{16-2ac}{2a^2}}$

Answer 1

The correct option is B $\frac{\sqrt{16-2ac}}{a}$

$H^2={\propto }^2+{\beta }^2$

${ax}^2-4x+c=0$

$\propto +\beta =\frac{-b}{a}=\frac{4}{a}$

$\propto \beta =\frac{c}{a}$

${(\propto +\beta )}^2=({\propto }^2+{\beta }^2)+2\propto \beta$

${\left(\frac{4}{a}\right)}^2=H^2+\frac{2c}{a}$

$H^2=\frac{16}{a^2}-\frac{2c}{a}$

$H=\frac{\sqrt{16-2ca}}{a}$