Q2 of 227 Page 82

Find a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively.

Formula for quadratic equation is,

x² – (sum of roots) x + Product of roots = 0

Given, sum of roots = and product of roots =

∴ Quadratic equation is,

⇒ x² – x – = 0

⇒ = 0

Hence, Quadratic equation is = 0.

Find a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively.

Find the quotient and remainder using synthetic division.

x³ + x² – 3x + 5) ÷ ( x – 1)