Question

if (x+y) is factor of each of the polynomials y^2+2y-15 and y^3+a find the values of k and a​

Answer 1

Step-by-step explanation:

let,

k+y=0 , y = - k

f (x) =y'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-5)=0

k=5 or -3

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

Thank u.