Question

6) Find a cubic polynomial whose zeros are 2, -3 and 4.
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Answer 1

Answer:

f(x) = x³ - 3x² - 10x + 24

Step-by-step explanation:

α= 2 ; β= -3; γ= 4

We know that,

α + β + γ= -b/a

2+(-3)+4 = -b/a

3 = -b/a

αβ + βγ + γα= c/a

2(-3)+ (-3)4 + 4(2) = c/a

-6 -12 + 8 = c/a

-10 = c/a

αβγ= -d/a

2×(-3)×4 = -d/a

-24= -d/a

The polynomial = [x³ -(α+β+γ)x² + (αβ+βγ+γα)x -αβγ]

= x³ - 3x² - 10x + 24