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.