Question:
If a and ??are the roots of 4x2 + 2x + 1 = 0, then ??=
If a and ??are the roots of 4x2 + 2x + 1 = 0, then ??=
Updated On: Jun 7, 2024
- $-\frac{1}{4\alpha}$
- $-\frac{1}{2\alpha}$
- $-\frac{1}{\alpha}$
- $-\frac{1}{3\alpha}$
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The Correct Option is A
Solution and Explanation
Given equation is
$4 x^{2}+2 x-1=0$
Roots of the equation are $\alpha$ and $\beta$.
$\therefore \alpha+\beta=\frac{-b}{a}=\frac{-2}{4}=-\frac{1}{2}$
and $ \alpha \beta=\frac{C}{a}=-\frac{1}{4}$
$\therefore \beta=-\frac{1}{4 \alpha} $
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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.
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There are basically four methods of solving quadratic equations. They are:
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- Using Quadratic Formula
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