Today, we are going to study topic Quadratic Equations. Equations which are of the form ax square

plus bx plus c equals to zero, are quadratic equations when a is not equal to zero. If a is zero than

equation is linear equation.

Let us talk about roots of quadratic equations. Alpha beta are the, if alpha beta are the roots of

equation ax square plus bx plus c is equal to zero, that means alpha beta satisfies then what can we

say, first thing that we can say is ax square plus bx plus c can be written as a into x minus alpha to x

minus beta. Why, because alpha is the root of this equation hence alpha satisfies ax square plus bx

plus c is equal to zero and hence x minus alpha is the factor of this quadratic polonomy. From this

we can derive that sum of the roots is minus b by a. From this we can easily see that what will come

from sum of this root, minus b by a. Product of this root is c by a and difference of roots of both the

equations is under root of b square minus 4ac by mod a. Difference of roots of this quadratic

equation is b square minus 4ac upon mod a. Other thing, we can see from here is as alpha is root

square of ax square plus bx plus c equals to zero, if alpha is one root then what will it do to it, it will

satisfy. Means after putting alpha in this, this equation will be satisfied.

Again, let me make you revise. Some of roots minus b by a, product of roots is c by a, difference of

roots is under root d by mod a, square root of discriminant. b square upon 4c is called discriminant,

you all know. And alpha will satisfy this equation. Similarly, beta will also satisfy this equation. A beta

square plus b beta plus c is equal to zero.

Yes, let us see how to use all these five reasons. Okay, take out question number 1 of your

worksheet. If 1 minus p is a root of quadratic equation x square plus px plus 1 minus p equals to

zero, then it’s roots are, if 1 minus p is one root then we have to find other two roots. Okay, if 1

minus p is its root then 1 minus p will satisfy this equation. What I have done here is, I have put 1

minus p instead of x, instead of x, I have put 1 minus p. From this take 1 minus p as common, from

here we get that p should be equal to 1. If p is 1 then this equation becomes x square plus x equals

to zero means what is its roots, x into x plus equals to zero, either x equals to zero or x equals to

minus 1. Hence both the roots are zero and minus 1, hence a is the correct answer. I hope everybody

got it.

Let us go to next question. The difference between corresponding roots of x square plus ax plus b

equals to zero and x square plus bx plus a equals to zero is same. The difference between both the

roots is same. What will the difference of first root? What is the formula of difference of roots?

What is mod a? Under root of discriminant upon mod a. What will be the roots of first equation?

What will be the discriminant of first equation? A square minus 4b upon, what is the coefficient of x

square is 1 upon mod of 1. And what will the difference of roots of second equation? B square minus

4a upon mod 1, hence you can say that a square minus 4b is equal to.