Question

Which of the following is not a zero of the polynomial $p\left(x\right)=x^3-11x^2+36x-36?$

• A. 2
• B. 3
• C. 4
• D. 6

Answer 1

The correct option is C 4

$x=a$ is a zero of the polynomial $p\left(x\right),ifp\left(a\right)=0.$

Given: $p\left(x\right)=x^3-11x^2+36x-36$

Taking $x=2:$

$p\left(2\right)=(2{)}^3-11\times (2{)}^2+36\times 2-36$

= 8 - 44 + 72 - 36

= 0

∴ 2 is a zero of $p\left(x\right)$.

Taking $x=3:$

$p\left(3\right)=(3{)}^3-11\times (3{)}^2+36\times 3-36$

= 27 - 99 + 108 - 36

= 0

∴ 3 is a zero of $p\left(x\right).$

Taking $x=4:$

$p\left(4\right)=(4{)}^3-11\times (4{)}^2+36\times 4-36$

= 64 - 176 + 108

$=-4\ne 0$

∴ 4 is not a zero of $p\left(x\right)$.

Taking $x=6:$

$p\left(6\right)=(6{)}^3-11\times (6{)}^2+36\times 6-36$

= 216 - 396 + 216 - 36

= 0

∴ 6 is a zero of $p\left(x\right)$.

Hence, the correct answer is option (c).