Mathematics Questions

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:

Solve: √(x+5) + √ x = 5.

If roots of ax^2 + bx + c = 0 are in ratio m:n, then:

The sum of a number and its reciprocal is 10/3. Find the number.

Find the values of k for which x^2 - (k+4)x + 2k + 5 = 0 has equal roots.

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

Solve for x: 3^(x+2) + 3^-x = 10.

The product of the roots of (a/b)x^2 + (b/c)x + (c/a) = 0 is: