Question

If a, a + b, a + 2b are zeroes of the cubic polynomial x³ – 6x² + 3x + 10, then a + b = ______.

Answer 1

If a, a + b, a + 2b are zeroes of the cubic polynomial x³ – 6x² + 3x + 10, then a + b = 2.

Explanation:

Let the roots be a, a + b, a + 2b.

By Vieta’s formulas the sum of the roots equals 6 (from x³ – 6x² + 3x + 10).

So 3a + 3b = 6

⇒ 3(a + b) = 6

⇒ a + b = 2