Question

For what values of m will the equation x²-2x(1+3m)+7(3+2m)=0 have equal roots?

Answer 1

`m=-10/9" or "m=2`

Explanation:

`"for the quadratic to have equal roots we require"`

`"the "color(blue)"discriminant "Delta=0`

`•color(white)(x)Delta=b^2-4ac`

`"with "a=1,b=-2(1+3m)=-2-6m`

`"and c=7(3+2m)=21+14m`

`rArr(-2-6m)^2-4(21+14m)=0`

`rArr4+24m+36m^2-84-56m=0`

`rArr36m^2-32m-80=0larrcolor(blue)"factorise"`

`rArr4(9m^2-8m-20)=0`

`rArr4(m-2)(9m+10)=0`

`"equate each factor to zero and solve for m"`

`m-2=0rArrm=2`

`9m+10=0rArrm=-10/9`