If the value of real number a> 0 for which \(x^2\)-5ax+1-0 and \(x^2-a x-5-0\) have a common real root is \(\frac{3}{\sqrt{2 \beta}}\) then \( \beta\) is equal to_______
If the value of real number a> 0 for which \(x^2\)-5ax+1-0 and \(x^2-a x-5-0\) have a common real root is \(\frac{3}{\sqrt{2 \beta}}\) then \( \beta\) is equal to_______
Correct Answer: 13
Approach Solution - 1
So, the correct answer is 13.
Approach Solution -2
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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