Final answer:
To find the discriminant of the function 7x² + 4 = 19x – 10, rearrange it to standard form, identify the coefficients, and then apply the formula b² - 4ac. The discriminant in this case is -31, which means the equation has two complex roots.
Step-by-step explanation:
The discriminant of a quadratic equation is found using the formula Discriminant = b² - 4ac, which is derived from the quadratic formula used to solve for the roots of the equation. For the given function 7x² + 4 = 19x – 10, we first need to rearrange it into the standard form ax² + bx + c = 0. To do so, we subtract (19x – 10) from both sides to get 7x² - 19x + 14 = 0.
The coefficients for this equation are a = 7, b = -19, and c = 14. We obtain the following when we enter these values into the discriminant formula:
Discriminant = (-19)² - 4(7)(14) = 361 - 392 = -31
The value of the discriminant for the given equation is -31, indicating that the equation has two complex roots.