Find the value of m so that the quadratic equation $mx( x-7) +49=0$ has two equal roots.
Given: An equation $mx( x-7) +49=0$.
To do: To find out the value of m for which the given equation has two equal roots.
Solution:
here given equation is $mx( x-7) +49=0$
$\Rightarrow mx^{2} -7mx+49=0$
On comparing it to quadratic equation $ax^{2} +bx+c=0$
Here we find that $a=m,\ b=-7m\ and\ c=49$
For the quadratic equation to have equal roots, ists discriminant D$=0$
Or $\sqrt{\left( b^{2} -4ac\right)} \ =0$
On substituting the values of $\ a,\ b\ and\ c$
$\sqrt{\left(( -7m)^{2} -4\times m\times 49\right)} =0$
$\Rightarrow \sqrt{\left( 49m^{2} -196m\right)} =0$
$\Rightarrow 49m^{2} -196m=0$
or $49\left( m^{2} -4m\right) =0$
$m^{2} -4m=0$
$\Rightarrow m( m-4) =0$
Either $m=0\ or\ m-4=0$ or $m=4$
$\therefore m=0,\ 4$
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