Q. 224.1( 27 Votes )
Obtain all zeros of f(x) = x3 + 13x2 + 32x + 20 if one of its zeros is –2.
Answer :
We know that if x = a is a zero of a polynomial then (x – a) is a factor of f(x)
Since –2 is zero of f(x). Therefore, (x + 2) is a factor of f(x).
Now on divide f(x) = x3 + 13x2 + 32x + 20 by (x + 2) to find other zeros.
By applying division algorithm, we have:
x3 + 13x2 + 32x + 20 = (x+2)(x2+11x+10)
We do factorisation here by splitting the middle term,
⇒ x3 + 13x2 + 32x + 20 = (x+2)(x2+11x+10)
⇒ x3 + 13x2 + 32x + 20 = (x+2)(x2+10x+x+10)
⇒ x3 + 13x2 + 32x + 20 = (x+2) {x(x+10)+1(x+10)}
⇒ x3 + 13x2 + 32x + 20 = (x+2) (x+10)(x+1)
Hence, the zeros of the given polynomial are: –2, –10, –1
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