Question

If the given expression $x^2-(5m-2)x+(4m^2+10m+25)$ can be expressed as a perfect square, then the value(s) of $m$ is/are

• A. $-\frac{4}{3}$
• B. $\frac{4}{3}$
• C. $8$
• D. $-8$

Answer 1

Answer: (A), (C)

The correct options are
A $-\frac{4}{3}$
C $8$

If the given expression $x^2-(5m-2)x+(4m^2+10m+25)$ can be rewritten as perfect square,
then the roots of equation $x^2-(5m-2)x+(4m^2+10m+25)=0$
will be equal.
$\therefore D=0\Rightarrow (5m-2{)}^2=4(4m^2+10m+25)\Rightarrow 25m^2-20m+4=16m^2+40m+100\Rightarrow 9m^2-60m-96=0\Rightarrow 3m^2-20m-32=0\Rightarrow (m-8\left)\right(3m+4)=0\therefore m=-\frac{4}{3},8$