Question

find the value of k , if y+3 is a factor of 3y^+ky+6

Answer 1

y+3=0
y=-3
p(y)=3y²+ky+6
p(-3)=3(-3)²+k(-3)+6
0=3*9-3k+6
0=27+6-3k
3k=33
k=33/3
k=11

The value of k is 11.

Answer 2

Solution :

If y+3 is a factor of the given polynomial 3y^2 + my + 6 = 0

→ y + 3 = 0

→ y = -3

Now , substitute the value of y in the given polynomial,

→ 3y² + ky + 6

→ 3(-3)² + (-3)k + 6 = 0

We equate the equation to zero, because the substitution of the factor always gives the value 0.

When solving the equation ,

→ 27 - 3k + 6 = 0

→ 3k = 33

→ K = 33/3

→ K = 11