Quadratic Equations

For what value of m is x^2 - mx + 1 = 0 a perfect square?

Find the value of k if the roots of x^2 - kx + 9 = 0 are equal.

The roots of the equation 3x^2 - 5x + 2 = 0 are:

If α and β are roots of x^2 - 5x + 6 = 0, find α^2 + β^2.

Find the quadratic equation whose roots are -3 and 4.

The discriminant of the equation √3x^2 + 10x - 8√3 = 0 is:

If the sum of the roots of 3x^2 + (2k+1)x - (k+5) = 0 is equal to the product of roots, then k is:

Solve for x: x + 6/x = 5.

The sum of a number and its square is 42. Find the number.

For what value of p does the equation px^2 - 4x + 3 = 0 have no real roots?

Solve for x: (x+3)^2 = 25.

If α and β are roots of 2x^2 - 4x + 1 = 0, find the value of 1/α + 1/β.

If the roots of x^2 - px + q = 0 differ by 1, then:

The product of two consecutive even numbers is 168. Find the numbers.

Find k if one root of x^2 - 8x + k = 0 is 3 times the other.

The roots of x^2 - 2√2x + 2 = 0 are:

If 4 is a root of x^2 - px + 12 = 0, what is the value of p?

If the roots of (k-1)x^2 - 10x + 3 = 0 are reciprocal, find k.

Solve: 2x^2 + x - 6 = 0.

Which of the following has real and equal roots?