Given g(x)=px+q where p and q are constants.If g^2(x)=16x+15 find the possible values of p and q?
I am confused by your data
if by g^2(x) you mean g(x)*g(x)
then it would be (px+q)^2
= p^2x^2 + 2pqx + q^2
but that was equal to 16x + 15
there was no x^2 term , so p=0
But that contradicts that 2pqx = 16x
To find the possible values of p and q in the equation g^2(x) = 16x + 15, we can start by expanding g^2(x) and then equating it to the given expression.
First, let's find what g^2(x) is equal to:
g^2(x) = (px + q)^2
= (px + q)(px + q)
= p^2x^2 + 2pqx + q^2
Now, we equate g^2(x) to the given expression 16x + 15:
p^2x^2 + 2pqx + q^2 = 16x + 15
To determine the values of p and q, we need to compare the coefficients on both sides of the equation.
1. Coefficient of x^2:
On the left side, we have p^2x^2, and on the right side, there is no term with x^2. This implies that p^2 = 0, and therefore p = 0.
2. Coefficient of x:
On the left side, we have 2pqx, and on the right side, we have 16x. Since the coefficients on both sides need to be equal, we can equate them:
2pq = 16
Since p = 0 (from the previous step), we have:
2 * 0 * q = 16
0 = 16
Therefore, the equation 0 = 16 is not true for any value of q. This means there are no valid solutions for q in this case.
So, the only value we've found is p = 0. There are no possible values for q that satisfy this equation: g^2(x) = 16x + 15.