Question

How many real roots does the quadratic function h(x) = 3x ^ 2 + 9x - 7 have?

Answer 1

The quadratic function h(x) = 3x^2 + 9x - 7 has two distinct real roots, as the discriminant calculated from its coefficients is positive.

Step-by-step explanation:

To determine how many real roots the quadratic function h(x) = 3x^2 + 9x - 7 has, we can use the discriminant of the quadratic equation, which is found using the formula b^2 - 4ac from the general form of a quadratic equation ax^2 + bx + c = 0.

In this case, a = 3, b = 9, and c = -7,

so the discriminant is 9^2 - 4(3)(-7) = 81 + 84

= 165.

Since the discriminant is positive, the quadratic function has two distinct real roots.

Answer 2

The quadratic function h(x) = 3x^2 + 9x - 7 has two real roots because the discriminant, calculated as b^2 - 4ac, is positive (165).

Step-by-step explanation:

To determine how many real roots the quadratic function h(x) = 3x^2 + 9x - 7 has, we need to calculate the discriminant of the quadratic equation, which is the part of the quadratic formula b^2 - 4ac under the square root. In this case, a = 3, b = 9, and c = -7. Plugging these values into the discriminant formula, we get:

Discriminant = b^2 - 4ac

Discriminant = 9^2 - 4(3)(-7)

Discriminant = 81 + 84

Discriminant = 165

Since the discriminant is positive (165), this means the quadratic function has two real roots. This aligns with the fact that a positive discriminant indicates two distinct real solutions in Two-Dimensional (x-y) Graphing.