Question

Find a cubic polynomial whose zeroes are 1 ,-2and 3

Answer 1

Step-by-step explanation:

form of a Cubic polynomial -

ax³ + bx² + cx + d = 0

x³ + (b/a)x² + (c/a)x + (d/a) = 0

Let the roots of this polynomial are p , q & r .

So , p + q + r = -b/a

1 - 2 + 3 = -b/a

4 - 2 = -b/a

b/a = -2

&. pq + qr + rp = c/a

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

-2 - 6 + 3 = c/a

c/a = -8+3 = -5

& also pqr = -d/a

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

-6 = -d/a

d/a = 6

At the end ,

The cubic polynomial is

x³ - 2x² - 5x + 6 = 0