Without trying to solve the equation 3x^2-5x+7=0, how would you know that it has no real roots?

Question

please help

Answer 1

The solutions of a quadratic equation ax² + bx + c = 0, a ≠ 0, can be classified as follows.If the discriminant b² - 4ac is

1. positive, then the quadratic equation has two distinct real solutions and its graph has two - intercepts.

2. zero, then the quadratic equation has one repeated real solution and its graph has one - intercept.

3. negative, then the quadratic equation has no real solutions and its graph has no - intercepts.

The quadratic equation is 3x² - 5x + 7 = 0.

Compare the equation 3x² - 5x + 7 = 0 with general form of quadratic equation ax² + bx + c = 0, a ≠ 0.

a = 3, b = - 5 and c = 7.

The discriminant =  b² - 4ac = (- 5)² - 4(3)(7) = 25 - 84 = - 59 < 0.

Here discriminant is negative, so the quadratic equation has no real roots.

Answer 2

The equation

Compare it to quadratic form

Roots are

The roots of are imaginary.

No real roots for .