Question

if x+5 is a factor of p(x) =x3-20x+5k,then k is​

Answer 1

Given

if x+5 is a factor of p(x) =x3-20x+5k,then k is

To find

Find the value of k

Solution

=> x + 5 = 0

=> x = -5

P(x) = x³ - 20x + 5k

=> x³ - 20x + 5k = 0

=> (-5)³ - 20 × (-5) + 5k = 0

=> -125 + 100 + 5k = 0

=> 5k = 25

=> k = 25/5 = 5

$\blue{\boxed{\sf{\red{Hence,\:k=5}}}}$

Answer 2

Given,

(x+5) is a factor of p(x) = x³-20x+5k

To find,

The value of k.

Solution,

The value of k will be 5.

We can easily solve this problem by following the given steps.

According to the question,

(x+5) is a factor of p(x) = x³-20x+5k

So, we have

(x+5) = 0

Moving 5 from the left-hand side to the right-hand side will result in the change of sign from plus to minus,

x = -5

When (x+5) is its factor then this value of x should make the value of the given polynomial to be 0.

Putting the value of x,

p(x) = x³-20x+5k

p(-5) = (-5)³-20(-5)+5k

p(-5) = -125+100+5k

p(-5) = 5k-25

Equating it with 0,

5k-25 = 0

5k = 25

k = 25/5

k = 5

Hence, the value of k is 5.