Quadratic Equations

The area of a rectangular field is 60 sq m. If its length is 7m more than its width, find the width.

The sum of the roots of 0.2x^2 - 0.4x + 0.1 = 0 is:

If the discriminant of x^2 + bx + 1 = 0 is negative, then:

If x^2 - 1/9 = 0, then x is:

Find the value of 'a' if roots of ax^2 + 2x + 1 = 0 are real.

If α, β are roots of x^2 - x - 1 = 0, find αβ.

The quadratic equation whose one root is 2 + √3 is:

If the roots of 4x^2 - 2x + k - 4 = 0 are reciprocal, find k.

Solve: (x-1)(x-2) = 2.

If the ratio of roots of x^2 + bx + c = 0 is 1:2, then:

The discriminant of (x+5)^2 = 0 is:

Solve for x: x^2 + 5x + 6 = 0.

If the roots of x^2 + px + 12 = 0 are in the ratio 1:3, find p.

The product of two consecutive integers is 20. Find the integers.

If α, β are roots of x^2 - 3x + 1 = 0, find α^2β + αβ^2.

If the roots of ax^2 + bx + c = 0 are equal in magnitude but opposite in sign, then:

If α and β are roots of x^2 - px + q = 0, find α/ β + β/ α.

Solve for x: x^4 - 13x^2 + 36 = 0.

Find k if one root of x^2 - (k+1)x + 12 = 0 is 3.

If the roots of x^2 - bx + c = 0 are two consecutive integers, then b^2 - 4c equals: