Question

If the equation $x^2-m(2x-8)-15=0$ has equal roots then $m=?$

• A. $3,-5$
• B. $-3,5$
• C. $3,5$
• D. $-3,-5$

Answer 1

The correct option is C

$3,5$

Explanation for correct option

We know that if the quadratic equation $a{x}^2+bx+c=0$ has equal root then $b^2-4ac=0$

Given equation is $x^2-m(2x-8)-15=0$

Now comparing with standard form we have

$a=1,b=-2m$ and $c=8m-15$

$$\begin{gathered} \therefore b^2-4ac=0 \\ \Rightarrow {\left(-2m\right)}^2-4\times \left(1\right)\times \left(8m-15\right)=0 \\ \Rightarrow 4m^2-32m+60=0 \\ \Rightarrow m^2-8m+15=0 \\ \Rightarrow m^2-3m-5m+15=0 \\ \Rightarrow m\left(m-3\right)-5\left(m-3\right)=0 \\ \Rightarrow \left(m-3\right)\left(m-5\right)=0 \\ \therefore m=3,5 \end{gathered}$$

Hence, option (C) is correct i.e. $3,5$