Question

if (k+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

Answer:

Here, the given polynomials are -

• p(y) = y² + 2y - 15
• q(y) = y³ + a

• (k+y) is the factor of each of the polynomial p(y) and q(y)

It means y = -k is a factor of given polynomial and p(-k) = 0 and q(-k) = 0.

p(-k) = (-k)² + 2(-k) = 15

→ 0 = k² - 2k - 15

→ 0 = k - 5k + 3k - 15

→ 0 = k (k-5) + 3 (k-5)

→ 0 = (k+3) (k-5)

•°• k = -3, 5

The values of k are -3 and 5.

q(-k) = (-k)³ + a

→ 0 = -k³ + a

→ k³ = a

→ (-3)³ = a

•°• a = -27

→ (5)³ = a

•°• a = 125

The values of a are -27 and 125.