Question

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1. Find all the zeroes of p(x)= x3-9x2-12x+20, if (x+2) is a factor of p(x).

Answer 1

Answer:

The zeroes are -2, 10 and 1.

Step-by-step explanation:

Given, polynomial,

$p(x)=x^3-9x^2-12x+20$

Since, (x+2) is a factor of p(x).

Thus, p(x) must be divisible by (x+2),

When we divide p(x) by x + 2,

The quotient is,

$x^2-11x+10$

Hence, we can write,

$x^3-9x^2-12x+20=(x+2)(x^2-11x+10)$

For zeroes,

p(x) = 0,

$\implies (x+2)(x^2-11x+10)=0$

$(x+2)(x^2-10x-x+10)=0$

$(x+2)(x(x-10)-1(x-10)=0$

$(x+2)(x-10)(x-1)=0$

Thus, zeroes of p(x) are -2, 10 and 1.

Answer 2

Answer:

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