math
posted by Melissa .
determine the value of k such that g(x)=3x+k intersects the quadratic function f(x)=2x^25x+3 at exactly one point
determine the value(s) of k such that the linear function g(x)=4x+k does not intersect the parabola f(x)=3x^2x+4

2x^2  5x + 3 = 3x + k
2x^2  8x + (3k) = 0
We want both roots of this to be the same. That is, it must be a perfect square.
2(x2)^2 = 2x^2  8x + 8
So, we want 3k=8 or k=5
SO, 3x5 intersects the parabola in exactly one point.

If the line does not intersect the parabola, then f(x)g(x) = 0 must have a negative discriminant.
The line intersects the parabola when
4x+k = 3x^2  x + 4
3x^2 + 5x + k4 = 0
5^2  4(3)(k4) = 25  12k + 48 = 73  12k < 0
7312k < 0
k > 73/12
Respond to this Question
Similar Questions

discrete math
1. let A and B be sets. Show that A U (B  A)=A U B 2. determine whether f is a function from Z to R if a) f(n)= +n b) 1/(n square 4) For 1. BA is the same as B intersect ~A (That's the complement of A) So A U B = A U (B int ~A) … 
math
How do I know that x^27=y is a function? 
Need Help!! Algebra
I am having trouble in this class and need help with this question.. What similarities and differences do you see between functions and linear equations studied Are all linear equations functions? 
Calculus AB
Analyze the function ln x=cx^2 to find the unique value of c such that there is exactly one solution to the equation. To do this find the value of c such that both sides of the equation have equivalent slopes at some point; this will … 
calc
analyze the function ln x = cx^2 to find the unique value of c such that there is exactly one solution to the equation. to do this, find the value of c such that both sides of the equation have equivalent slopes at some point; this … 
Calculus
Let f be a twicedifferentiable function such that f(2)=5 and f(5)=2. Let g be the function given by g(x)= f(f(x)). (a) Explain why there must be a value c for 2 < c < 5 such that f'(c) = 1. (b) Show that g' (2) = g' (5). Use … 
Math
determine the value of k such that g(x)=3x+k intersects the quadratic function f(x)+2x^25x+3 
Math Help!
A.) Determine "a" and "k" so both points are on the graph of the function. 1.) (0,1) (2,1); y=a(x1)^2+k 2.) (1,11) (2,19); y=a(x+1)^2+k B.) Determine whether or not the function f(x)=0.25(2x15)^2+15 has a mazimum or a minimum value. … 
Math
A quadratic function is defined by f(x)=3.7x^2+6.8x+4.2. A linear function is defined by g(x)=0.5x+k. Determine the value of k so that the line intersects the parabola at exactly one point. Write your answer to the nearest hundredth 
Algebra
Two graph never intersect. As such, the equation has no solutions. Create an equation where the left side is a linear function and the right side is a square root function. Make it so that the equation has exactly one solution.