Question
Find a cubic polynomial whose zeroes are $2, -3$ and $4$
✓
Answer
If the zeroes of the cubic polynomial are a, b and c then the cubic polynomial can be found as:
$x^3- (a + b + c)x^2 + (ab + bc + ca)x - abc ...(1)$
Let $a = 2, b = -3$ and $c = 4$
Substituting the values in (1), we get
$x^3 - (2 - 3 + 4)x^2 + (-6 - 12 + 8)x - (-24)$
$\Rightarrow x^3 - 3x^2 - 10x + 24$
$x^3- (a + b + c)x^2 + (ab + bc + ca)x - abc ...(1)$
Let $a = 2, b = -3$ and $c = 4$
Substituting the values in (1), we get
$x^3 - (2 - 3 + 4)x^2 + (-6 - 12 + 8)x - (-24)$
$\Rightarrow x^3 - 3x^2 - 10x + 24$
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