Question

Verify whether the following are zeros of the polynomial normal indicated against them
p(z)=z²+z-6 at z= -3​

Answer 1

Step-by-step explanation:

Given

$p(z) = z {}^{2} + z - 6$

$z = - 3$

$substitute \: in \: p(z)$

$p(z) = ( - 3) {}^{2} - 3 - 6$

$= 9 - 9$

$= 0$

$so \: z = - 3 \: is \: the \: zero \: of \: given \: equation$

Answer 2

Given,

The polynomial, p(z) = z²+z-6

z = -3

To find,

The verification whether -3 is a zero of the given polynomial.

Solution,

We can easily solve this problem by following the given steps.

According to the question,

The polynomial, p(z) = z²+z-6

z = -3

To check it for the given polynomial, this value should make the value of the polynomial to be zero.

Now, putting the value of z in polynomial,

p(z) = z²+z-6

p(-3) = (-3)²+(-3)-6

p(-3) = 9-3-6

p(-3) = 9-9 [The integers with the negative sign are added but the result remains negative.]

p(-3) = 0

Hence, it is verified that the value of z as -3 is the zero of the polynomial, p(z) = z²+z-6.