Question:

The roots of the equation x4 + x3 - 4x2 + x + 1 = 0 are diminished by h so that the transformed equation does not contain x2 term. If the values of such h are α and β, then 12(α - β)2 =

Updated On: Oct 22, 2024
  • 35

  • 25

  • 105

  • 115

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The Correct Option is A

Solution and Explanation

The correct option is: (A) 35
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Concepts Used:

Quadratic Equations

A polynomial that has two roots or is of degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b, and c are the real numbers

Consider the following equation ax²+bx+c=0, where a≠0 and a, b, and c are real coefficients.

The solution of a quadratic equation can be found using the formula, x=((-b±√(b²-4ac))/2a)

Two important points to keep in mind are:

  • A polynomial equation has at least one root.
  • A polynomial equation of degree ‘n’ has ‘n’ roots.

Read More: Nature of Roots of Quadratic Equation

There are basically four methods of solving quadratic equations. They are:

  1. Factoring
  2. Completing the square
  3. Using Quadratic Formula
  4. Taking the square root