Answer: the discriminant of the quadratic equation 9x² + 2 = 10x is 28.
Step-by-step explanation: To find the discriminant of the quadratic equation 9x² + 2 = 10x, we need to use the formula for the discriminant, which is b² - 4ac, where a, b, and c are the coefficients of the quadratic equation.
In this case, the quadratic equation is in the form ax² + bx + c = 0, where a = 9, b = -10, and c = 2.
Now, let's substitute these values into the formula for the discriminant:
Discriminant = (-10)² - 4(9)(2)
Calculating further:
Discriminant = 100 - 72
Discriminant = 28
It's worth noting that the discriminant is a value that helps us determine the nature of the roots of a quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If it is zero, the equation has one real root (a perfect square). And if it is negative, the equation has no real roots (complex roots). In this case, the discriminant is positive (28), indicating that the equation has two distinct real roots.
