Nature of Roots of a Quadratic Equation

Find the sum of the roots of the equation x² –  8x + 2 = 0

If the roots of equation 3x² + 2x + (p + 2) (p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?

Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)² - 3x + 4 = 0

Find the positive value(s) of k for which quadratic equations x² + kx + 64 = 0 and x² – 8x + k = 0 both will have real roots ?

Without solving, examine the nature of roots of the equation 2x² + 2x + 3 = 0

Find the value of k for which equation 4x² + 8x – k = 0 has real roots.

Solve for x: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`

Find the values of k for which the roots are real and equal in each of the following equation:

2kx² - 40x + 25 = 0