RBSE Class 10 Maths Notes Chapter 4 Quadratic Equations

These comprehensive RBSE Class 10 Maths Notes Chapter 4 Quadratic Equations will give a brief overview of all the concepts.

RBSE Class 10 Maths Chapter 4 Notes Quadratic Equations

1. Quadratic Equation – An equation in which the greatest exponent of the unknown quantity (x, y, z) be 2 is called a quadratic equation. For example ax² + bx + c = 0. If b = 0, then the form of the equation will be ax² + c = 0.
It is such a quadratic equation in which there is no linear term of x. Such type of a quadratic equation in which there is no linear term of the unknown quantity is called a pure quadratic equation.

2. In variable x a quadratic equation is of the form ax² + bx + c = 0, where a, b, c are real numbers and a + 0.

3. A real number a is called a root of the quadratic equation ax² + bx + c = 0, if aa² + + c = 0. The zeroes of the quadratic polynomial ox² + bx + c and the roots of the quadratic equation ax² + bx + c = 0 are the same.

For example
In the equation x² + 5x + 6 = 0
Putting x = – 2, (- 2)² + 5(- 2)+ 6 = 4- 10 + 6 = 0
Putting x = – 3, (- 3)² + 5(- 3)+ 6 = 9-15 + 6 = 0
Hence – 2 and – 3 will be called the roots of the quadratic equation ax² + bx + c = 0.

Note –
(i) In the above example – 2 and – 3 are the roots of the equation x² + 5x + 6 = 0, not the zeroes.
(ii) Zeroes are related with polynomial whereas the roots are related with the equation.

4. If we can factorise ax² + bx + c, a + 0 into two linear factors, then the roots of the quadratic equation ax² + bx + c = 0 can be obtained by equating each factor to zero.

5. A quadratic equation can also be solved by the method of completing the square.

6. Quadratic Formula – The roots of the quadratic equation ax² + bx + c = 0 are given by
\(x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}, \text { if } b^{2}-4 a c \geq 0\)

7. In a quadratic equation or² + bx + c = 0, a ≠ 0

• There are two distinct real roots, if b² – 4ac >0
• Two equal real roots (i.e., coincident real roots), if b² – 4ac = 0 and
• no real roots, if b² – 4ac < 0

8. If p(x) is a quadratic polynomial, then p(x) = 0 is called a quadratic equation. The standard form of a quadratic equation is ax² + bx + c = 0 where a, b, c ∈ R and a ≠ 0

9. If p(x) =. 0 is a quadratic equation then the zeroes or solution of the polynomial p(x) will be the roots or solution of the equation p(x) = 0.

10. If the roots of a quadratic equation are given as a, p and we are to find out the quadratic equation, then we use the following formula – x² – (sum of roots) x + product of roots = 0
i.e x² – (α + β) x + αβ = 0