Question

Check whether 3 and –2 are the zeros of the polynomial p(x) when p(x) = x² – x – 6.

Answer 1

A zero or root of a polynomial function is a number that, when plugged in for the variable, makes the function equal to zero.
Now,
P(x) = x² – x – 6
Therefore,
P(-2) = (-2)² – (-2) – 6
⇒ P(-2) = 4 + 2 – 6
⇒ P(-2) = 0

similarly, P(3) = 3² – 3 – 6
⇒ P(3) = 9 – 3 – 6
⇒ P(3) = 0
Hence, Yes, 3 and -2 are zeroes of the polynomial x² – x – 6.

Answer 2

#AlexaRousey here!!

Any number (a) is a zero of polynomial p(x) if p(a) = 0.

Hence if p(3) = 0 & p(-2) = 0 there are roots of p(x).

=) p(3) = 3^2 - 3 - 6

= 9 - 9

= 0

& =) p(-2) = (-2)^2 - (-2) - 6

= 4 + 2 - 6

= 0

Hence 3 nd - 2 are the zeroes of polynomial p(x) when p(x) = x² – x – 6.

Thanks!!