Quadratic Equations

For what value of k are the roots of kx^2 + 4x + 1 = 0 real?

If one root is 2 + sqrt(3), then the other root of a quadratic equation with rational coefficients is:

The roots of the equation (x-a)(x-b) = 0 are:

Sum of roots of the equation x^2 - 9 = 0 is:

If the discriminant is a perfect square, the roots are:

The equation x^2 + x - 1 = 0 has roots that are:

Find the value of p if the roots of 3x^2 - px + 3 = 0 are equal.

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

If α and β are roots of x^2 + bx + c = 0, then α^2 + β^2 is:

Find the product of the roots of the equation (x-5)(x+2) = 10.

The roots of ax^2 + bx + c = 0 are real if:

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

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

The sum of a number and its reciprocal is 2. The quadratic equation is:

If x^2 + 5x + 6 = 0, find the value of (1/α + 1/β) where α, β are roots.

A room is 3m longer than it is wide. If the area is 40 sq. m, find the width.

The discriminant of √2x^2 + 7x + 5√2 = 0 is:

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

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

If the equation (k-1)x^2 + (k+1)x + (k-1) = 0 has real and equal roots, find k.