The sum of the values of $x$ satisfying the equation, $\sqrt{x}\left(\sqrt{x}-4\right)-3\left|\sqrt{x}-2\right|+6=0 \left(x\,\ge\,0\right),$ is :
- $26$
- $10$
- $25$
- $8$
The Correct Option is A
Solution and Explanation
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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:
- Factoring
- Completing the square
- Using Quadratic Formula
- Taking the square root