Question

The value of 'm' for which the equation (1+m) x²-2(1+3m) x +(1+8m) =0 has equal roots, is Х​

Answer 1

We know –

• If Δ (Discriminant) >0here are two separate real roots.
• If Δ (Discriminant) =0, there are two identical real roots.
• If Δ (Discriminant) <0, there are no real roots, but there are two complex roots.

Question's given –

The equation (1+m) x²-2(1+3m) x +(1+8m) =0 has equal roots.That means, Δ Discriminant is 0.(D= b²-4ac)

According to the question –

• a = (1+m)
• b = -2(1+3m)
• c = (1+8m)

Now, Δ Discriminant = 0

↠{-2(1+3m)}² -4 × (1+m) ×(1+8m)=0

↠4(1+3m)² - 4 (1+m)(1+8m) = 0

↠4(1+ 9m² + 6m - 1 -8m - m -8m²) =0

↠4 (1+ 9m² + 6m - 1 -9m -8m²)=0

↠m²-3m =0

↠m(m-3) = 0

↠m =0,3

• Henceforth, value of m will be 0 or 3.