Question

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

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Answer 1

Given that the equation x

2

−2x(1+3m)+7(3+2m)=0 have equal roots.

The given equation have equal roots only if the discriminant is zero

⇒b

2

−4ac=(2+6m)

2

−4(21+14m)=0

⇒4+36m

2

+24m−56m−84=0

⇒36m

2

−32m−80=0

⇒9m

2

−8m−20=0

⇒m=2,−

9

10