A and B are positive roots of quadratic equation and (A + B)2 = 400 and (A – B)2 = 4. Find the quadratic equation whose roots are A and B.

A and B are positive roots of quadratic equation and (A + B)2 = 400 and (A – B)2 = 4. Find the quadratic equation whose roots are A and B. Correct Answer x² – 20x + 99

Given,

⇒ (A + B)² = 400

⇒ (A – B)² = 4

Solving and taking square roots as A and B are positive, we get

⇒ A + B = 20

⇒ A – B = 2

Now, adding both the above equation, we get,

⇒ 2A = 22

⇒ A = 11

Now,

⇒ 11 + B = 20

⇒ B = 9

Now,

⇒ Product of roots = AB = 99

⇒ Sum of roots = 20

So, quadratic equation is,

⇒ x² – (sum of roots)x + product of roots = 0

⇒ x² – 20x + 99 = 0