Question

the numerical value of side of a cube of volume 64cm 3 is the zero of 2x²+5x+k, then =​

Answer 1

Answer:

k=-52

Step-by-step explanation:

volume of cube is a^3,

a^3=64

a^3=4^3

a=4

2x^2+5x+k=0

2(4)^2+5(4)+k=0

2(16)+20+k=0

32+20+k=0

52+k=0

k=-52

Answer 2

Given data:

The numerical value of a side of a cube of volume $64\:cm^{3}$ is the zero of $2x^{2}+5x+k$

To find:

The value of $k$

Step-by-step explanation:

Given, the volume of the cube is $64\:cm^{3}$

Then the length of a side of it

$=\sqrt[3]{64}\:cm$

$=\sqrt[3]{4^{3}}\:cm$

$=4\:cm$

Given that the numerical value of $4\:cm$, that is, $4$ is a zero of $2x^{2}+5x+k$, then

$\quad 2(4^{2})+5(4)+k=0$

$\Rightarrow 32+20+k=0$

$\Rightarrow k=-52$

Final answer:

The value of $k$ is $(-52)$.