Question

If -1 and 2 are the two zeros of the polynomial x3-4x2-7x+10 find the third zero

Answer 1

note that the zeroes should be x = 1 and x = - 2 not x = - 1 and x = 2

the factors are then ( x - 1 ) and (x + 2)

and x³ - 4x² - 7x + 10 = (x - 1 )(x + 2) = x² + x - 2

thus x² + x - 2 is a factor

dividing x³ - 4x² - 7x + 10 by x² + x - 2 gives x - 5

the third zero is x = 5

check : (5)³ -4(5)² - 7(5) + 10 = 125 - 100 - 35 + 10 = 0