Question:
If b$^2 \ge 4 ac$ for the equation $ax^4 + bx^2 + c = 0$, then all the roots of the equation will be real if
If b$^2 \ge 4 ac$ for the equation $ax^4 + bx^2 + c = 0$, then all the roots of the equation will be real if
Updated On: Jun 23, 2023
- b>0, a<0, c>0
- b<0, a>0, c>0
- b>0, a>0, c>0
- b>0, a>0, c<0
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The Correct Option is C
Solution and Explanation
Given : $ax^4 + bx^2 + c + 0$
Equation will be real if D $\ge$ 0
$\Rightarrow b^2 - 4ac \ge 0 \Rightarrow b^2 \ge 4ac$
Equation will be real if D $\ge$ 0
$\Rightarrow b^2 - 4ac \ge 0 \Rightarrow b^2 \ge 4ac$
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Concepts Used:
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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