Question

For what integer value/s of m, the quadratic equation $x^2-mx+5m=0$ has real and distinct roots.

• A. $m=0orm=20$
• B. $m=0orm>20$
• C. $0<m<20$
• D. $m<0orm>20$

Answer 1

The correct option is D $m<0orm>20$

$5x^2-mx+2m=0$

$a=5,b=-m,c=2m$

Since the quadratic equation has real and distinct roots,

$D=b^2-4ac>0$

$(-m{)}^2-4\times 5m>0$

$m^2-20m>0$

$m(m-20)>0$

It is of the form (x-a) (x-b) > 0 and a < b, then

$x<aorx>b$

$\Rightarrow m<0orm>20$

$\text{(d) is corrrect}$