Question

If 3y^2+ py^2+ 4y + q has a factor y + 2 and gives remainder -5 if it divided by (y - 3). Find the value of p and q.

Answer 1

The value of p is -8 and the value of q is 28

Given : The polynomial $3y^{2} +py^{2} +4y +q$ has a factor y +2 and gives the remainder -5 when divided by y -3

To Find : The value of p and q

Solution : The value of p is -8 and the value of q is 28

It is given that the polynomial  $3y^{2} +py^{2} +4y +q$ has a factor y +2 and gives the remainder -5 when divided by y -3

This mean that y = -2 is a zero of the polynomial

that is $(3+p) (-2)^{2} +4(-2)+q = 0$

(3+p)4 -8 +q = 0

4p +q = -4  equation 1)

Now the polynomial gives the remainder -5 when divided by y-3

So by dividing the polynomial  $3y^{2} +py^{2} +4y +q$ by y - 3 by long division we get

quotient (3+p)y +(13+3p) and remainder 39 +9p+q

and remainder is equal to -5

so  39 +9p+q = -5

39 +9p+q = -5

9p +q = -44 equation 2)

Solving equation 1) and equation 2) we get '

9p +q = -44

4p +q = -4

-     -      +

5p = -40 p = -8

and q = 28

So the value of p is -8 and the value of q is 28  

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