Question:

The roots of the equation $\begin{vmatrix}0&x&16\\ x&5&7\\ 0&9&x\end{vmatrix} = 0 $ are :

Updated On: Apr 9, 2024
  • 0, 12 and 12
  • 0 and $\pm$12
  • 0, 12 and 16
  • 0, 9 and 16
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The Correct Option is B

Solution and Explanation

Given $\begin{vmatrix}0&x&16\\ x&5&7\\ 0&9&x\end{vmatrix} = 0 $ $\Rightarrow \ 0 (5x - 63) - x (x^2 - 0) + 16 (9x - 0) = 0 $ $\Rightarrow \ - x^3 + 144x = 0 $ $\Rightarrow \ x (144 - x^2) = 0 $ $\Rightarrow \ x = 0, \pm 12. $
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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