Question

Obtain all zeros of polynomial x cube + 13 x square + 32 x + 20 if one of its zeros is -2

Answer 1

Answer:

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Step-by-step explanation: Let p(x) = x^3 + 13x^2 + 32x + 20

Using Hidden Trial Method,

On putting x = -1 in p(x) , we get

→(-1)^3 + 13×(-1)^2+32 × -1 + 20

→ -1+13-32+20

→-33+33

→0

so,(x+1) is a factor of p(x).

Then,on dividing p(x) by(x+1) using long division method ,we obtain the quotient = x^2+12x+20

Now, factorising x^2+12x+20 by splitting the middle term ,

→  x^2 + (10 + 2) x +20

→ x^2 + 10x + 2x + 20

→ x(x+10) + 2 (x+10)

→ (x+10) (x+2)

Thus , all the zeroes of p(x) are (x+1) , (x+2) and (x+10)