Question

7. Find the roots of the equation x² + ax - bx - ab = 0​

Answer 1

Group all the coefficients together

x2−(a+b)x+ab=0

Use the quadratic formula

x=a+b±(a+b)2−4ab√2

Now note that

(a+b)2−4ab=a2+b2+2ab−4ab=a2+b2−2ab=(a−b)2

and therefore

x=a+b±(a−b)2√2=a+b±(a−b)2

Explicitly we get

x+=a+b+(a−b)2=a

x−=a+b−(a−b)2=b