Question

For the following function, h(x) = 2x^2 + 3x - 14: (a) Find the values of x for which h(x) = 0. (b) Find h(0) Express numbers using integers or simplified fractions.

Answer 1

To solve the equation h(x) = 0, we can use the quadratic formula. The values of x for which h(x) = 0 are -14/4 and 2. To find h(0), we substitute x = 0 into the function and get -14.

Step-by-step explanation:

To find the values of x for which h(x) = 0, we need to solve the quadratic equation 2x^2 + 3x - 14 = 0. We can do this by factoring or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = 3, and c = -14.

Substituting these values into the formula, we get:

x = (-3 ± √(3^2 - 4(2)(-14))) / (2(2))

Simplifying further:

x = (-3 ± √(9 + 112)) / 4

x = (-3 ± √121) / 4

x = (-3 ± 11) / 4

So the values of x for which h(x) = 0 are x = -14/4 and x = 8/4 = 2.

To find h(0), we substitute x = 0 into the function:

h(0) = 2(0)^2 + 3(0) - 14 = 0 + 0 - 14 = -14.