Quadratic Equations and Inequations in Class 11
You'll learn the basic steps in finding the roots of a quadratic equation using the formula, I recommend using the formula only when you find it difficult to find the roots of a quadratic equation directly.
Nature of the roots of a quadratic equation
Once you find the roots of a quadratic equation using the formula, you'll learn about the Discriminant. You can determine the nature of the roots of a quadratic equation using the Discriminant. Note that, if the discriminant is greater than zero, the roots are unequal and irrational or rational, depending on whether the discriminant is a perfect square.
If the Discriminant is equal to zero, the roots are equal. If the discriminant is lesser than zero, the roots are complex or imaginary. You have a number of problems based on this concept.
Sum and Product of the roots of a quadratic equation
You'll learn how to calculate the sum and product of the roots of a quadratic equation using a simple formula. This formula enables you to find the sum and product of the roots of a quadratic equation without actually calculating the roots. Again, this is a very important formula, with tremendous applications, and also asked in SAT examinations.
In this context, learn cases when the roots are reciprocal of each other, one root is unity, the roots are equal and more. Moving on, you'll learn about the sign of the quadratic equation. Note that in a quadratic equation, if a is positive, we have an upward facing parabola and if a is negative, we have a downward facing parabola.
Learn how to solve Quadratic Inequalities.This is, in fact the most important part of this chapter. You'll need to learn what is a quadratic inequality and the concept of open and closed interval.
Learn how to solve a quadratic inequality by finding the roots, dividing the number line into intervals and identifying the solution.
This topic has applications in Derivatives and Calculus, so make sure you get it right. An important point to note is that this method works only if the coefficient of the highest power of x is positive. If not, you have to make it positive, by multiplying with -1.
Another important point to remember is that when you have powers of roots, if the power is odd, then the above method of dividing into intervals will not work.
Learn how to solve quadratic inequalities expressed as a quotient. You need to note that if the quotient is negative, cross multiplying will change the inequality. What you need to do is multiply both sides by the square of the denominator.
Solving Quadratic inequalities video
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