Question

For what value of m are the roots of the quadratic equation Xsq-2x (1+3m)+7 (3+2m)=0 equal

Answer 1

m = − or m = 2
Explanation:
for the quadratic to have equal roots we require
the discriminant Δ = 0
∙ x Δ = b 2 − 4ac
with a = 1, b = − 2(1 + 3m) =
− 2 − 6m
and c = 7(3 + 2m) = 21
+ 14m
⇒ ( − 2 − 6m) 2
− 4(21 + 14m) = 0
⇒ 4 + 24m + 36m 2 − 84
− 56m = 0
⇒ 36m 2 − 32m − 80 = 0
← factorise
⇒ 4(9m 2 − 8m − 20) = 0
⇒ 4(m − 2)(9m + 10) = 0
equate each factor to zero and solve for m
m − 2 = 0 ⇒ m = 2
9m + 10 = 0 ⇒ m = -10/9