Quadratic Equations

What is the sum of the roots of the quadratic equation \(2x^2 - 5x + 3 = 0\)?

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

The quadratic equation \(x^2 + px + 16 = 0\) has equal roots. Find the value of \(p\).

Find the roots of the quadratic equation \(3x^2 - 2x - 1 = 0\).

If the roots of \(x^2 - 7x + m = 0\) differ by 3, find \(m\).

The quadratic equation \(kx^2 - 4x + 1 = 0\) has equal roots. Find \(k\).

If \(\alpha\) and \(\beta\) are roots of \(x^2 - 3x + 2 = 0\), find the quadratic equation whose roots are \(\frac{1}{\alpha}\) and \(\frac{1}{\beta}\).

The quadratic equation \(x^2 + bx + 16 = 0\) has roots \(2 + \sqrt{3}\) and \(2 - \sqrt{3}\). Find \(b\).

Find the value of \(k\) if \(x^2 + kx + 25 = 0\) has real roots.

If the roots of \(x^2 - 4x + m = 0\) are in the ratio 3:1, find \(m\).