F as f(x):px^2+qx-5 for the total of x.If f(-1)=1 and f(1)= -9,find a)value of p and q b)valuesof x when f(x)=1

Question

please help me to find the answer it is so hard for me plus confusing

Answer 1

Let y=f(x)=px^2+qx-5 and plug in (-1,1) and (1,-9):

1=p-q-5; p-q=6

-9=p+q-5; p+q=-4

Add these two equations together: 2p=10 so p=5 and q=-1.

f(x): 5x^2-x-5, so when f(x)=1, 5x^2-x-5=1 and 5x^2-x-6=0=(5x-6)(x+1). So x=6/5 or -1.