Question

if K+Y) is a factor of the each of the polynomial y2+2y-15 and y3+a. find the value k and a?

Answer 1

Let k+y=0.y=-k.
f(x)=y^2+2y-15
f(-k)=(-k)^2+2y-15
=k^2-2k-15
Given: k+y is a factor. Therefore, remainder should be=0.
Which means:
k^2-2k-15=0
k^2-5k+3k-15=0
k(k-5)+3(k-5)=0
(k-5)(k+3)=0
k=5 or -3.
Next:
f(y)=y^3+a
f(-k)=-k^3+a
Again:
Remainder should be=0
-k^3+a=0
When value of k is taken 5:
-(5)^3+a=0
-125+a=0
a=125
When the value of x is taken as -3:
-(-3)^3+a=0
27+a=0
a=-27

Answer 2

Answer:

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