Question

The equation $x^2+2(m-1)x+(x+5)=0$ has real and equal roots. Find the value of $m$.

Answer 1

Given the equation $x^2+2(m-1)x+(x+5)=0$ or, $x^2+(2m-1)x+5=0$......(1) has real and equal roots.

Then the discreminant $=0$

or, $(2m-1{)}^2-\mathrm{4.5.1}=0$

or, $4m^2-4m-19=0$

or, $m=\frac{4\pm \sqrt{4^2+\mathrm{4.4.19}}}{2.4}$

or, $m=\frac{4\pm 4\sqrt{1+19}}{2.4}$

or, $m=\frac{1\pm \sqrt{20}}{2.4}$

or, $m=\frac{1\pm 2\sqrt{5}}{2}$.