Question

the roots of quadratic equation x^2+5x-(alpha+1)(alpha+6)=0, where alpha is a?​

Answer 1

Step-by-step explanation:

x² + 6x - x - (α + 1)(α + 6) = 0

⇒ x² + (α + 6)x - (α + 1)x - (α + 1)(α + 6) = 0

⇒ x[x + (α + 6)] - (α + 1)[x + (α + 6)] = 0

⇒ [x - (α + 1)][x + (α + 6)] = 0

⇒ [x - (α + 1)] = 0, [x + (α + 6)] = 0

⇒ x = α + 1, -(α + 6)