Here, you will learn about

i. How to solve a quadratic equation, using the formula. You can also solve it by direct factorization, but what happens if the correct factors don't click in your mind. You are introduced to the basic formula to find the roots of a x^2+bx+c=0, which is (-b plus or minus sqrt(b^2-4ac))/2a . Some of the questions discussed are

Solve sqrt(2) x^2+x+sqrt(2)=0

Find x , if p+7=0, q-12=0 , x^2+px+q=0

Solve (x-2)/(x+2) +(x+2)/(x-2)=4

Solve x^(2/3)-x^(1/3)-2=0

ii. What happens if the equation is not a quadratic? Then you will learn how to convert it to a quadratic. Have a look at these problems to understand how. These are discussed in the second lesson.

Solve sqrt(3x+1)-sqrt(x-1)=2

Solve (sqrt(x^2+1)-sqrt(x^2-1))/(sqrt(x^2+1)+sqrt(x^2-1))=1/3

Solve sqrt(x/y)+sqrt(y/x)=5/2

iii. You will learn how to calculate the nature of the roots of a quadratic equation. A few of the problems discussed include

Discuss the nature of the roots of x^2-(p+1)x+ p=0, p is a rational number

If a, b, c are rational numbers, show that the roots of a x^2+bx +c =0 are rational

iv. You will also be introduced to finding the sum and product of the roots of a quadratic equation. You can learn problems of the type

Write the sum and product of the roots of sqrt(2) x^2-sqrt(2)x+4=0

If the roots of x^2+ p x +7 = 0 are a, b and a^2 +b^2 =22, find p

If a, b are the roots of x^2 +k x+ 12 = 0, and a -b = 1, find k

I hope this course helps you to understand this topic better. Thank you and wish you all the best in your learning!