Question:
Let $x^2 + \alpha x + \beta = 0$ the equation whose roots are the negatives of the roots of $x^2 + 7x - 2 = 0$ then the value of $\alpha + \beta$ is
Let $x^2 + \alpha x + \beta = 0$ the equation whose roots are the negatives of the roots of $x^2 + 7x - 2 = 0$ then the value of $\alpha + \beta$ is
Updated On: Jun 23, 2023
- 5
- -5
- 9
- -9
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The Correct Option is D
Solution and Explanation
We have,
$x^2 + a x + ? = 0$ be the equation whose roots are the negative of the roots of $x^2 + 7x - 2 = 0 $
$? a = - 7$
and $? = - 2$
$a + ? = (-7 ) +(-2) = -9$
$x^2 + a x + ? = 0$ be the equation whose roots are the negative of the roots of $x^2 + 7x - 2 = 0 $
$? a = - 7$
and $? = - 2$
$a + ? = (-7 ) +(-2) = -9$
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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