Mathematics Worksheet: Quadratic Equations

Quadratic Equations

• The roots of the quadratic equation x² + 4x + 6 = 0 are irrational.
• For the quadratic equation 4x² + kx + 25 = 0 to have equal roots, the value of 'k' is ±10.
• The quadratic equation whose sum and product of the roots is -1 and 1, respectively, is 4x² + x + 1 = 0.

Complex Roots

• If 2 + 3i is a root of the equation x² + ax + b = 0, then the values of (a, b) are (4, -13).

Properties of Quadratic Equations

• If α and β are roots of the quadratic equation x² + kx + 2 = 0 and αβ = 1, then the value of k is 3.
• If a and β are roots of the quadratic equation px² + qx + r = 0, then the sum of the roots is -q/p.
• For the quadratic equation ax² + bx + c = 0 to have roots in the ratio m : n, the condition is mnb² = ac(m + n)².
• If one root is equal to the square of the other root of the equation x² + x - k = 0, then the value of k is 2.
• If a and β are roots of the quadratic equation ax² - ax + b = 0, then α + β is 2.
• If a and β are roots of the quadratic equation x² - p(x + 1) + c = 0, then (1 + a)(1 + β) is c.