File Name: relation between roots and coefficient of polynomial equations .zip
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The quotient rule is a formula for finding the derivative of a fraction.
Summary: In algebra you spend lots of time solving polynomial equations or factoring polynomials which is the same thing. It would be easy to get lost in all the techniques, but this paper ties them all together in a coherent whole. This is the Factor Theorem : finding the roots or finding the factors is essentially the same thing. The main difference is how you treat a constant factor.
We have seen that the b 2 - 4 ac portion of the quadratic formula, called the discriminant , can tell us the type of roots of a quadratic equation. The quadratic formula can also give us information about the relationship between the roots and the coefficient of the second term and the constant of the equation itself. Consider the following:. We can also see these relationships emerge from factoring the quadratic equation. The roots will be represented as r 1 and r 2. But, let's put our new formulas to use and apply the relationship between the roots and the coefficients and constants.
Often the words "zeroes" and "roots" will be used interchangeably. However, they are not the same thing, and it is good to understand the difference. Why are these terms used interchangeably sometimes? Because if you set a polynomial equal to zero, you have a polynomial equation, and that equation's roots are the same as the polynomial's zeroes. In this section we're going to deal strictly with polynomial equations in which a polynomial is set equal to zero. We're going to begin by looking at some quadratic equations, and explore the relationship between the coefficients and the roots. From there, we will expand the concept to higher degree polynomials.
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Relation between roots and coefficients of any polynomial equation. IN THIS CHAPTER.
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To find the conditions when roots are connected by given relations. Sometimes the relation between roots of a quadratic equation is given and we are asked to find the condition i. This will clear when you go through illustrative examples.
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