By using the definition of second order polynomials and the discriminant from quadratic formula, we conclude that the values of k must be less than 1/4.

<h3>How to determine the value of k such that a line intersects a quadratic equation</h3>

In this question we must determine the set of values of k such that the function g(x), a linear function, intersects a quadratic function f(x) at two points. In this case, we must solve the following second order polynomial:

k · x² + 4 · x - 3 - g(x) = 0

k · x² + 4 · x - 3 - 2 · x + 7 = 0

k · x² + 2 · x + 4 = 0

In this case, the discriminant of the equation described above must be positive:

2² - 4 · k · 4 > 0

4 - 16 · k > 0

4 > 16 · k

16 · k < 4

k < 1/4

By using the definition of second order polynomials and the discriminant from quadratic formula, we conclude that the values of k must be less than 1/4.

To learn more on quadratic equations: brainly.com/question/17177510

#SPJ1

5 0

2 years ago