Question

f(x)=x^2+4x+1 and g(x)=3x+d... for what values of d does the equation f(x)=g(x) produce one solution?

Answer 1

\[x^2+4x+1=3x+d\]subtract and get
\[x^2+x+1-d=0\]
it will have one solution if the discriminant \(b^2-4ac\) is 0. set
\[1^2-4\times (1-d)=0\] and solve for \(d\)

Answer 2

then what does it mean by "find the value of d when eq f(x)=g(x) produce 2 solutions"?

Answer 3

two solutions means the discriminant is positive
solve
\[1-4(1-d)>0\] which should be real easy if you have already solved
\[1-4(1-d)=0\]

Answer 4

thanks

Answer 5

yw