# Higher Algebra Hall & Knight Indeterminate Equations of the Second Degree (Chapter 28) Solutions

Hall and Knight Higher Algebra Solutions Chapter 28 ‘Indeterminate Equations of the Second Degree’ have been prepared to assist you in solving these advanced level exercise questions effortlessly. In this chapter of Higher Algebra by Hall and Knight you will learn to solve the indeterminate equations of the first degree using the properties of recurring continued fractions learnt in the previous chapter using numerical examples of this chapter. The topics covered in this chapter are solutions of ax^{2} +2hxy+by^{2}+2gx+2fy+c=0, evaluation of the general solution of x^{2}-Ny^{2 }= 1, and solution of x^{2}– Ny^{2 }= – 1. Besides all the above topics, you will also get to know the steps to find the solutions of x^{2}-n^{2}y^{2}=a and diophantine problems.

There are 22 questions in Hall & Knight Algebra Book Indeterminate Equations of the Second Degree covered in 1 exercise. The questions will help you attain complete clarity in the concepts of indeterminate equations and the different methods to find their solutions. This chapter holds importance not only in Class 12 but also for entrance exams like IIT JEE and NEET. You will get acquainted with the most commonly occurring maths problem in your competitive exams and in your higher studies. The questions can be solved only with good conceptual clarity in the topics. We advise you to take guidance from Instasolv’s Hall & Knight Algebra Mathematics book with solutions.

The expert team of mathematicians at Instasolv has created this set of solutions for Higher algebra by Hall and Knight with great care. We have used simple and understandable language for explaining the concepts of Indeterminate Equations of the First Degree. You will find assistance at every step with precise reasoning. The solutions of this classic algebra book have been written in a format strictly compliant to the latest guidelines for competitive exams.

## Important Topics Covered under Hall and Knight Higher Algebra Solutions Chapter 28: Indeterminate Equations of the Second Degree

**Introduction**

Indeterminate Equations of the Second Degree hold practical importance because it is related to the Theory of Numbers. The chapter discusses the indeterminate equations of the second degree consisting of 2 variables in detail.

**Values of x and y that satisfy ****a****x ^{2 }**

**+ 2hxy + b**

**y**

^{2 }**+ 2gx + 2fy + c = 0**

We can obtain the values of x and y in the form of positive integrals in the equation of the form, ax^{2 }+ 2hxy + by^{2 }+ 2gx + 2fy + c = 0 such that a, b, c, f, g, h are integers.

If x and y are positive integers under the radical denoted as.

py2+2qy+r=z2, solving it in y following rules of a quadratic equation,

If this expression is an exact square, say t^{2}, then

t^{2} – pz^{2} = q^{2 }– pr such that t and z are the variables and p, q, and r are constants.

### Exercise Discussion of Hall and Knight Higher Algebra Solutions Chapter 28: Indeterminate Equations of the Second Degree

- There is 1 exercise with 22 questions in this chapter covering all the topics such as solutions of ax
^{2 }+ 2hxy +by^{2}+ 2gx + 2fy + c = 0, evaluation of the general solution of x^{2}– Ny^{2 }= 1, solution of x^{2}– Ny^{2 }= -1, solutions of x^{2 }– n^{2}y^{2}= a and diophantine problems. - We have provided stepwise solutions for each exercise problem of Hall & Knight Higher Algebra Indeterminate Equations of the Second Degree.

## Why Use Hall and Knight Higher Algebra Solutions Chapter 28: Indeterminate Equations of the Second Degree by Instasolv?

- All the questions of Higher Algebra By H.S. Hall and S.R. Knight have been solved in a step by step format for absolute clarity in the concepts and formulae used.
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- The solutions are precise and on-point. You may use these solutions directly in your homework or for quick revision before your exams.
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