Question

write the polynomial whose zeroes are 4 and -2?

Answer 1

sum of zeroes = 4 + (-2) = 2product of zeroes = 4 x -2 = -8
general formula for quadratic equation
k(x² -(sum of zeroes)x + (product of zeroes))k(x² - 2x + (-8))k(x² - 2x - 8)
here k = 1so the equation is
x²-2x - 8

Answer 2

The polynomial whose zeroes are 4 and -2 is $x^{2} - 2x - 8$

• Equation of polynomial with a, b as roots is

                    $x^{2} - (a+b)x + ab$  -----------(1)

• Here a = 4, b = -2
• Substituting above values in (1)

                           $x^{2} - (4-2)x + (4)(-2)\\x^{2} - 2x - 8$