Question:
The solution of the equation $ 2{{x}^{3}}-{{x}^{2}}-22x-24=0 $ when two of the roots are in the ratio $ 3:4, $ is
The solution of the equation $ 2{{x}^{3}}-{{x}^{2}}-22x-24=0 $ when two of the roots are in the ratio $ 3:4, $ is
Updated On: Jun 23, 2024
- $ 3,\,4,\frac{1}{2} $
- $ -\frac{3}{2},-2,4 $
- $ -\frac{1}{2},\frac{3}{2},2 $
- $ \frac{3}{2},2,\frac{5}{2} $
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The Correct Option is B
Solution and Explanation
Given equation is
$ 2{{x}^{3}}-{{x}^{2}}-22x-24=0 $
On putting
$ x=0,1,-1,2,-2 $ only $ x=-2 $
satisfies this equation.
So, $ x=-2 $
is a root of this equation and from the given options only [b] has this root.
$ 2{{x}^{3}}-{{x}^{2}}-22x-24=0 $
On putting
$ x=0,1,-1,2,-2 $ only $ x=-2 $
satisfies this equation.
So, $ x=-2 $
is a root of this equation and from the given options only [b] has this root.
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Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the 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.
