Question

if one zero of a cubic polynomial 3x3+5x2-9x+k is 0 what is k

Answer 1

SOLUTION

GIVEN

One zero of the below cubic polynomial is 0

$\sf{3 {x}^{3} + 5 {x}^{2} - 9x + k}$

TO DETERMINE

The value of k

EVALUATION

Let p(x) be the given polynomial

$\sf{p(x) = 3 {x}^{3} + 5 {x}^{2} - 9x + k}$

Since 0 is a zero of the polynomial

$\sf{ \therefore \: \: p(0) = 0}$

$\sf{ \implies 3. {(0)}^{3} + 5. {(0)}^{2} - 9.0+ k = 0}$

$\sf{ \implies 0 + 0 - 0+ k = 0}$

$\sf{ \implies k = 0}$

FINAL ANSWER

The required value of k is 0

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