Linear Inequalities In One Variable

Given equation are

%7B%7Bx%7D%5E%7B3%7D%7D%2B2%7B%7Bx%7D%5E%7B2%7D%7D-5x%2B2%3D0

?(i) and

%7B%7Bx%7D%5E%7B3%7D%7D%2B%7B%7Bx%7D%5E%7B2%7D%7D-8x%2B4%3D0

..(ii) Now, for finding GCD of the given equations

%7B%7Bx%7D%5E%7B3%7D%7D%2B%7B%7Bx%7D%5E%7B2%7D%7D-8x%2B4)%7B%7Bx%7D%5E%7B3%7D%7D%2B2%7B%7Bx%7D%5E%7B2%7D%7D-5x%2B2(1

%5Cbegin%7Balign%7D%20%26%20%7B%7Bx%7D%5E%7B3%7D%7D%2B%7B%7Bx%7D%5E%7B2%7D%7D-8x%2B4%20%5C%5C%20%26%20%5C%2C%5C%2C%5C%2C--%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%2B%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C-%20%5C%5C%20%26%20%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%20%5C%5C%20%26%20%7B%7Bx%7D%5E%7B2%7D%7D%2B3x-2)%7B%7Bx%7D%5E%7B3%7D%7D%2B%7B%7Bx%7D%5E%7B2%7D%7D-8x%2B4(x-2%20%5C%5C%20%5Cend%7Balign%7D

%5Cbegin%7Balign%7D%20%26%20%7B%7Bx%7D%5E%7B2%7D%7D%2B3%7B%7Bx%7D%5E%7B2%7D%7D-2x%20%5C%5C%20%26%20-%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C-%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%2B%20%5C%5C%20%26%20%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%20%5C%5C%20%26%20-2%7B%7Bx%7D%5E%7B2%7D%7D-6x%2B4%20%5C%5C%20%26%20-2x-6x%2B4%20%5C%5C%20%26%20%2B%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%2B%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C-%20%5C%5C%20%26%20%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%20%5C%5C%20%5Cend%7Balign%7D

Thus, GCD or common root of given equations is

%7B%7Bx%7D%5E%7B2%7D%7D%2B3x-2%3D0

%5Ctherefore

x%3D%5Cfrac%7B-3%5Cpm%20%5Csqrt%7B%7B%7B(3)%7D%5E%7B2%7D%7D-4%5Ctimes%201%5Ctimes%20(-2)%7D%7D%7B2%5Ctimes%201%7D

%5CRightarrow

x%3D%5Cfrac%7B3%5Cpm%20%5Csqrt%7B9%2B8%7D%7D%7B2%7D

%5CRightarrow

x%3D%5Cfrac%7B-3%5Cpm%20%5Csqrt%7B17%7D%7D%7B2%7D

%5CRightarrow

x%3D%5Cfrac%7B-3%2B%5Csqrt%7B17%7D%7D%7B2%7D%2C%5C%2C%5C%2C%5Cfrac%7B-3-%5Csqrt%7B17%7D%7D%7B2%7D

%5Ctherefore

Sum of roots

%3D%5Cfrac%7B-3%2B%5Csqrt%7B17%7D%7D%7B2%7D%2B%5Cfrac%7B-3-%5Csqrt%7B17%7D%7D%7B2%7D

%3D%5Cfrac%7B-6%7D%7B2%7D%3D-3

About Linear Inequalities In One Variable - J-K-CET

Linear Inequalities In One Variable is a vital chapter for J-K-CET aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.

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Review the topic breakdown to see which sub-topics within Linear Inequalities In One Variable carry the most weight. Then, tackle the questions iteratively to solidify your understanding.

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

About Linear Inequalities In One Variable - J-K-CET

Frequently Asked Questions

Why focus on Linear Inequalities In One Variable PYQs?

How to best use this analysis?

Linear Inequalities In One Variable

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

About Linear Inequalities In One Variable - J-K-CET

Frequently Asked Questions

Why focus on Linear Inequalities In One Variable PYQs?

How to best use this analysis?

Chapter Questions
2 MCQs