7. Form a cubic polynomial with zeroes 3, 2 and -1. (2)

1.	7. Form a cubic polynomial with zeroes 3, 2 and -1. (2)
Answer» Let the cubic polynomial be p(x) It's zeros are 3,2,-1 So the factors will be (x-3),(x-2),(x+1) A cubic polynomial will at most have three zeros So by multiplying all its three factors, we will get the polynomial (x-3)(x-2)(x+1) =(x²-2x-3x+6)(x+1) =(x²-5x+6)(x+1) =x³+x²-5x²-5x+6x+6 =x³-4x²+x+6

Answer»

Let the cubic polynomial be p(x)

It's zeros are 3,2,-1

So the factors will be (x-3),(x-2),(x+1)

A cubic polynomial will at most have three zeros

So by multiplying all its three factors, we will get the polynomial

(x-3)(x-2)(x+1)

=(x²-2x-3x+6)(x+1)

=(x²-5x+6)(x+1)

=x³+x²-5x²-5x+6x+6

=x³-4x²+x+6

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