CBSE Class 10 Maths Quadratic Equations – Get here the Notes for CBSE Class 10 Maths Quadratic Equations. Candidates who are ambitious to qualify the Class 10 with good score can check this article for Notes. This is possible only when you have the best CBSE Class 10 Maths study material and a smart preparation plan. To assist you with that, we are here with notes. Hope these notes will help you understand the important topics and remember the key points for exam point of view. Below we provided the Notes of CBSE Class 10 Maths for topic Quadratic Equations.

**Class:**10th**Subject:**Maths**Topic:**Quadratic Equations**Resource:**Notes

## CBSE Notes Class 10 Maths Quadratic Equations

Candidates who are pursuing in CBSE Class 10 are advised to revise the notes from this post. With the help of Notes, candidates can plan their Strategy for particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for CBSE Class 10 Maths Quadratic Equations from this article.

**QUADRATIC EQUATIONS**

The polynomial of degree two is called quadratic polynomial and equation corresponding to a quadratic polynomial P(x) is called a quadratic equation in variable x.

Thus, P(x) = ax^{2} + bx + c =0, a ≠ 0, a, b, c ∈ R is known as the standard form of quadratic equation.

There are two types of quadratic equation.

(i)** Complete quadratic equation :** The equation ax^{2} + bx + c 0 where a ≠ 0, b ≠ 0,c ≠ 0

(ii) **Pure quadratic equation :** An equation in the form of ax^{2} = 0, a ≠ 0, b = 0, c = 0

**ZERO OF A QUADRATIC POLYNOMIAL**

The value of x for which the polynomial becomes zero is called zero of a polynomial

For instance,

1 is zero of the polynomial x^{2} — 2x + 1 because it become zero at x = 1.

**SOLUTION OF A QUADRATIC EQUATION BY**

**FACTORISATION**

A real number x is called a root of the quadratic equation ax^{2} + bx + c =0, a 0 if aα^{2} + bα + c =0.In this case, we say x = α is a solution of the quadratic equation.

**NOTE:**

1. The zeroes of the quadratic polynomial ax^{2} + bx + c and the roots of the quadratic equation ax^{2} + bx + c = 0 are the same.

2. Roots of quadratic equation ax^{2} + bx + c =0 can be found by factorizing it into two linear factors and equating each factor to zero.

**SOLUTION OF A QUADRATIC EQUATION BY COMPLETING THE SQUARE**

By adding and subtracting a suitable constant, we club the x^{2} and x terms in the quadratic equation so that they become complete square, and solve for x.

In fact, we can convert any quadratic equation to the form (x + a)^{2} — b^{2} = 0 and then we can easily find its roots.

**DISCRIMINANT**

The expression b^{2} — 4ac is called the discriminant of the quadratic equation.

**SOLUTION OF A QUADRATIC EQUATION BY DISCRIMINANT METHOD**

Let quadratic equation is ax^{2} + bx + c = 0

**Step 1.** Find D = b^{2} — 4ac.

**Step 2.**

(i) If D > 0, roots are given by

x = -b + √D / 2a , -b – √D / 2a

(ii) If D = 0 equation has equal roots and root is given by x = -b / 2a.

(iii) If D < 0, equation has no real roots.

**ROOTS OF THE QUADRATIC EQUATION**

Let the quadratic equation be ax^{2} + bx + c = 0 (a ≠ 0).

Thus, if b^{2} — 4ac ≥ 0, then the roots of the quadratic

—b ± √b^{2} — 4ac / 2a equation are given by

**QUADRATIC FORMULA**

—b ± √b^{2} — 4ac / 2a is known as the quadratic formula

which is useful for finding the roots of a quadratic equation.

**NATURE OF ROOTS**

(i) If b^{2} — 4ac > 0, then the roots are** real and distinct.**

(ii) If b^{2} — 4ac = 0, the roots are** real and equal or coincident.**

(iii) If b^{2} — 4ac <0, the roots are not** real (imaginary roots)**

**FORMATION OF QUADRATIC EQUATION WHEN TWO ROOTS ARE GIVEN**

If α and β are two roots of equation then the required quadratic equation can be formed as x^{2} — (α + β)x + αβ =0

**NOTE :**

Let α and β be two roots of the quadratic equation (ax^{2} + bx + c = 0 then

**Sum of Roots:** – the coefficient of x / the coefficient t of x^{2} ⇒ α + β = – b / a

**Product of Roots :**

αβ = constant term / the coefficient t of x^{2} ⇒ αβ = c / a

**METHOD OF SOLVING WORD PROBLEMS**

**Step 1:** Translating the word problem into Mathematics form (symbolic form) according to the given condition

**Step 2 :** Form the word problem into Quadratic equations and solve them.

### Class 10 Key Points, Important Questions & Practice Papers

Hope these notes helped you in your schools exam preparation. Candidates can also check out the Key Points, Important Questions & Practice Papers for various Subjects for Class 10 in both Hindi and English language form the link below.

Class 10 Maths | कक्षा 10 गणित |

Class 10 Science | कक्षा 10 विज्ञान |

Class 10 Social Science | कक्षा 10 सामाजिक विज्ञान |

Class 10 English |

### Class 10 NCERT Solutions

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### Class 10 Mock Test / Practice

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### Class 10 Exemplar Questions

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