Quadratics

What is the sum of the roots of the quadratic equation 2x² - 5x + 3 = 0?

If one root of the quadratic equation x² - 6x + k = 0 is 2, find the value of k.

The quadratic equation 3x² + px + 12 = 0 has roots in the ratio 2:3. Find the value of p.

Find the vertex of the parabola given by y = 2x² - 8x + 5.

For the quadratic equation x² + bx + 16 = 0, if the roots are equal, find b.

If the roots of x² - 7x + m = 0 are consecutive integers, find m.

Find the discriminant of the quadratic equation 5x² - 4x + 1 = 0 and determine the nature of roots.

If the quadratic equation x² + px + q = 0 has roots α and β such that α² + β² = 10 and α + β = 3, find the value of q.

Solve the quadratic equation 2x² + 3x - 5 = 0 using the quadratic formula.

The quadratic equation x² - (k+1)x + k = 0 has equal roots. Find the value of k.