Question

What is the product of all constants k such that the quadratic x^2 + kx + 15 can be factored in the form (x + a)(x + b), where a and b are integers?

a) 10
b) 15
c) 20
d) 25

Answer 1

The product of all constants k such that the quadratic x^2 + kx + 15 can be factored in the form (x + a)(x + b) is 15.

Step-by-step explanation:

This quadratic equation can be factored in the form (x + a)(x + b) if the product of the constants k equals 15.

Let's expand the equation:

x^2 + kx + 15 = (x + a)(x + b)

Expanding the right side, we get:

x^2 + (a + b)x + ab

Comparing the coefficients, we can see that a + b = k and ab = 15.

So, one possible set of values for a and b is 1 and 15. Therefore, the product of all constants k is 1 * 15 = 15.