Question

Given: f(x) = kx² + 3kx − 4, what values of k would be needed for the function to have two real roots?

Answer 1

To find the values of k that would give the function two real roots, we can use the discriminant of the quadratic equation.

Step-by-step explanation:

To find the values of k that would give the function two real roots, we can use the discriminant of the quadratic equation. The discriminant is given by the formula b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0. In this case, a = k, b = 3k, and c = -4. For the function to have two real roots, the discriminant must be greater than zero. So we can write the inequality:

3k² - 4k > 0

Now we can solve this inequality to find the values of k that satisfy it.

k(3k-4)>0

=> 3k-4= 0

=> k = 4/3