Question

find a cubic polynomial whose zeroes are 1, -2, 3​

Answer 1

Answer:

Given zeroes are 1,-2,3

Step-by-step explanation:

let the zeores be a,b,c

Required polynomial expression for three zeroes is (x-a)(x-b)(x-c)=0

So, (x-1)(x+2)(x-3)=0

=(x-1)(x²-3x+2x-6)=0

=x³-3x²+2x²-6x-x²+3x-2x+6 =0

=x³-2x²-5x+6

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Answer 2

Step-by-step explanation:

Let - p , q & r are the three roots of a cubic polynomial ax³ + bx² + cx + d = 0

x³ + (b/a)x² + (c/a)x + (d/a) = 0

According to the question

p + q + r = -b/a

1 + (-2) + 3 = -b/a

4 - 2 = -b/a

b/a = -2

Now , pq + qr + rp = c/a

(1)(-2) + (-2)(3) + 3(1) = c/a

-2 + (-6) + 3 = c/a

c/a = -8+3 = -5

& pqr = -d/a

1(-2)(3) = -d/a

-6 = -d/a

d/a = 6

Now , the cubic polynomial is

x³ - 2x² - 5x + 6 = 0