Question

obtain all zeroes of the polynomial f(x)=x3+13x2+32x+20 if one of it's zeroes is -2

Answer 1

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Answer 2

Answer:

The all zeroes of the polynomial are -10, -2 and -1.

Step-by-step explanation:

The given polynomial is

$f(x)=x^3+13x^2+32x+20$

It is given that -2 is a zero of the function. It means (x+2) is a factor of given polynomial.

Divide f(x) by (x+2), to find the remaining factor.

Using long division method, we get

$\frac{x^3+13x^2+32x+20}{x+2}=x^2+11x+10$

The function can be written as

$f(x)=(x+2)(x^2+11x+10)$

$f(x)=(x+2)(x^2+10x+x+10)$

$f(x)=(x+2)(x(x+10)+1(x+10))$

$f(x)=(x+2)(x+10)(x+1)$

Equate f(x)=0, to find the zeros.

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

$x=-2,-10,-1$

Therefore all zeroes of the polynomial are -10, -2 and -1.