Find the sum and product of the root for the quadratic equation x2+4=0
Find the sum and product of the root for the quadratic equation x2+4=0
2,2
-2,2
-0,4
0,-4
The Correct Option is C
Solution and Explanation
To find the sum and product of the roots for the quadratic equation \(x^2+4=0\), we use Vieta's formulas, which relate the coefficients of a quadratic equation to the sum and product of its roots. For any quadratic equation of the form \(ax^2+bx+c=0\), the sum of the roots (\(S\)) is given by \(-b/a\) and the product of the roots (\(P\)) is given by \(c/a\).
Given equation: \(x^2+4=0\)
Here, \(a=1\), \(b=0\), and \(c=4\).
- Sum of the roots: \(S=-b/a=-0/1=0\)
- Product of the roots: \(P=c/a=4/1=4\)
Thus, the sum and product of the roots are \(0\) and \(4\), respectively. Therefore, the correct option is -0,4.
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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