Question

obtain all zeros of f(x)=x³+13x²+32x+20 if one of its zeros is -2​

Answer 1

Answer:

GIVEN POLYNOMIAL :–

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

IT'S ONE ROOT IS -2 , THAT'S IT'S DIVIDED BY ( X + 2 ).

SO , NEW FUNCTION –

$g(x) = {x}^{2} + 11x + 10$

$g(x) = {x}^{2} + 10x + x + 10$

$g(x) = x(x + 10) + 1(x + 10)$

$g(x) = (x + 1)(x + 10)$

SO REMAINING ROOTS ARE -1 , -10

Answer 2

Answer:

The answer will be -2, -1, -10 as it is said to obtain all the answers.

Step-by-step explanation:

Let the zeroes of the polynomial be α, β and γ.

According to the question,

α = -2, implies that (x + 2) = 0

f(x) = x³ + 13x² + 32x + 20

Therefore,

x³ + 13x² + 32x + 20 / x + 2

= x² + 11x + 10.

Therefore,

g(x) = x² + 11x + 10

       = x² + 10x + x + 10

       = x(x + 10) + (x + 10)

       = (x + 10)(x + 1)

Therefore, the zeroes of the given polynomials are -2, -1 and -10.

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