Question

Beta are the zeros of the quadratic polynomial p(x) = x²+x-2 find the value of 1/alpha -1/beta.

Answer 1

 ɪꜰ α and β are the roots of Quadratic Equation ax² + bx + c = 0 then :

Sum of the roots : α + β = -b/a

Product of the roots : α × β = c/a

Given that α and β are the zeros of Polynomial P(x) = x² - x - 4

⇒ α and β are the Roots of Quadratic Equation :  x² - x - 4 = 0

Here a = 1 and b = -1 and c = -4

⇒ Sum of the Roots : α + β = -b/a = -(-1)/1 = 1

⇒ Product of the Roots : αβ = c/a = -4/1 = -4

The Question is Find the Value of α²β + αβ²

α²β + αβ² can be written as αβ(α + β)

⇒ α²β + αβ² = -4(1) = -4