Solving Quadratic Equations
Now if you look at the questions that you typically get in this chapter – there will be two types of questions, in any algebra topic there are going be two types of questions: ‘Flexible Questions’ that is variable based, where all the roots and coefficients are given to you in terms of alphas, betas As, Bs, and Cs, which are very easy to solve by simple substitution. We will see that while solving the questions. And the other ones are ‘Fixed Questions’, where the numbers are given to you and you need to do a calculation to arrive at the answer. You will basically see four types of questions – Flexible Questions are very easy; we will just substitute and solve. You wouldn’t even need to practice anything over there. We will be very clear when we solve a question. In fixed questions, there are four types of questions that you will get. The first type is questions based on range of X, in that case you use a graph to solve the question. Right? If you have questions based on range of X – use a graph. If you have a question based on nature of roots, you use the value of d, that is second types of question. Third type is based on relation between roots and coefficients; there you use alpha plus beta and alpha-beta. And finally the direct question where quadratic equation is given to you and you are asked is to find the roots – use the quadratic formula. Right? –b ± √( d)/2a – that is it. These are the only four types of questions that you will get. So you either use a graph whenever it’s about a range of where X lies – you use a graph; whenever it’s about nature of the roots – are they real, are they complex – use value of d. Wherever you are given something about the roots and ask something about the coefficients – chose alpha+ beta, alpha-beta. And finally if you are directly given equation and asked to find the roots – use the quadratic formula. Those are the four types of questions that you will get. Let’s now start solving these questions.