Question

Check whether 3 and -2 are the zeroes of the polynomial p(x) when p(x) =x²-x-6.​

Answer 1

Taking 3 as x,

= ( 3 )² - 3 - 6 = 9 - 9 = O

Taking -2 as x,

= ( -2 ) ² - ( -2) - 6 = 4 + 2 - 6 = 0

Thus, both 3 & -2 are the zeros of the polynomial

Answer 2

given zeroes = 3, -2

polynomial p(x) = x² - x - 6

For polynomials,

x² - (sum of zeroes)x + (product of zeroes)

= x² - [ 3 + (-2) ]x + [ 3 × (-2) ]

= x² - [ 1 ]x + [ -6 ]

= x² - x - 6

Therefore, we can say that 3 and -2 are the zeroes of the polynomial x² - x - 6