Question

If α and β are the zeroes of the polynomial p(x) = x² − ax − b, then the value of (α + β + αβ) is equal to ______.

Options

• a + b

• − a − b

• a − b

• − a + b

Answer 1

If α and β are the zeros of the polynomial p(x) = x² − ax − b, then the value of (α + β + αβ) is equal to a − b.

Explanation:

p(x) = x² − ax − b

From Vieta’s formulas, we know:

Sum of the roots: α + β = a

Product of the roots: αβ = −b

Now, calculating:

= α + β + αβ 

= a + (−b)

= a − b