we want 2x^2 - 5x + 3 = 3x + k
2x^2 - 8x + 3-k = 0
Now, this equation has solutions as long as the discriminant is not negative
64 - 8(3-k) >= 0
40 + 3k >= 0
So, you can pick any value for k >= -40/3.
Think of the graphs. You have a parabola that open up, and a line with slope=3. If the line is too low, it will never touch the parabola. Raise it high enough, and it will always intersect the parabola, which extends upward forever.
Now, if you want a specific k, then you need to specify where the line intersects, or the slope at the intersection, or something.
determine the value of k such that g(x)=3x+k intersects the quadratic function f(x)+2x^2-5x+3
1 answer