Question:
The zeros of the polynomial $p(x)=x^{2}+x-6$ are
(a) 2,3
(b) $-2,3$
(c) $2,-3$
(d) $-2,-3$
Solution:
The given polynomial is $p(x)=x^{2}+x-6$.
Putting x = 2 in p(x), we get
$p(2)=2^{2}+2-6=4+2-6=0$
Therefore, x = 2 is a zero of the polynomial p(x).
Putting x = –3 in p(x), we get
$p(-3)=(-3)^{2}-3-6=9-9=0$
Therefore, x = –3 is a zero of the polynomial p(x).
Thus, 2 and –3 are the zeroes of the given polynomial p(x).
Hence, the correct answer is option (c).