For what values of m, the equation x2 – 2(1 + 3m)x + 7(3 + 2m) = 0 w

1.	For what values of m, the equation x2 – 2(1 + 3m)x + 7(3 + 2m) = 0 will have equal roots?
Answer» The given equation will have equal roots if its discriminant is 0. Here ∆ =[(–2(1 + 3m)]² – 4 (1) [7 + (3 + 2m)] = 4(1 + 9m² + 6m) – 28(3 + 2m) = 9m² – 8m – 20 = (m – 2) (9m + 10) Hence ∆ =0 ⇔ m = 2, −10/9

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

Answer»

The given equation will have equal roots if its discriminant is 0.

Here ∆ =[(–2(1 + 3m)]² – 4 (1) [7 + (3 + 2m)]

= 4(1 + 9m² + 6m) – 28(3 + 2m)

= 9m² – 8m – 20

= (m – 2) (9m + 10)

Hence ∆ =0 ⇔ m = 2, −10/9

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

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