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If the discriminant of a quadratic equation ax^2 + bx + c = 0 is positive (i.e., b^2 – 4ac > 0), then the roots of the quadratic equation are real and unequal.

This is because the discriminant is used to determine the nature of the roots of a quadratic equation. Specifically, if the discriminant is positive, then the roots of the quadratic equation are real and unequal. This is because in this case, the quadratic formula (-b ± sqrt(b^2 – 4ac)) / 2a will yield two distinct real solutions for x.

The given quadratic equation is:

122x^2 – 7x + 4 = 0

We can find the sum of the roots of this equation using the formula:

sum of roots = -b/a

If the discriminant of a quadratic equation ax^2 + bx + c = 0 is positive (i.e., b^2 – 4ac > 0), then the roots of the quadratic equation are real and unequal.

This is because the discriminant is used to determine the nature of the roots of a quadratic equation. Specifically, if the discriminant is positive, then the roots of the quadratic equation are real and unequal. This is because in this case, the quadratic formula (-b ± sqrt(b^2 – 4ac)) / 2a will yield two distinct real solutions for x.

In contrast, if the discriminant is zero (i.e., b^2 – 4ac = 0), then the roots of the quadratic equation are real and equal. This is because the quadratic formula will yield a single real solution for x.

If the discriminant is negative (i.e., b^2 – 4ac < 0), then the roots of the quadratic equation are complex conjugates. This means that the roots will have the form of a+bi and a-bi, where a and b are real numbers and i is the imaginary unit.