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.
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) = ax2 + 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 ax2 + bx + c 0 where a ≠ 0, b ≠ 0,c ≠ 0
(ii) Pure quadratic equation : An equation in the form of ax2 = 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
1 is zero of the polynomial x2 — 2x + 1 because it become zero at x = 1.
SOLUTION OF A QUADRATIC EQUATION BY
A real number x is called a root of the quadratic equation ax2 + bx + c =0, a 0 if aα2 + bα + c =0.In this case, we say x = α is a solution of the quadratic equation.
1. The zeroes of the quadratic polynomial ax2 + bx + c and the roots of the quadratic equation ax2 + bx + c = 0 are the same.
2. Roots of quadratic equation ax2 + 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 x2 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 — b2 = 0 and then we can easily find its roots.
The expression b2 — 4ac is called the discriminant of the quadratic equation.
SOLUTION OF A QUADRATIC EQUATION BY DISCRIMINANT METHOD
Let quadratic equation is ax2 + bx + c = 0
Step 1. Find D = b2 — 4ac.
(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 ax2 + bx + c = 0 (a ≠ 0).
Thus, if b2 — 4ac ≥ 0, then the roots of the quadratic
—b ± √b2 — 4ac / 2a equation are given by
—b ± √b2 — 4ac / 2a is known as the quadratic formula
which is useful for finding the roots of a quadratic equation.
NATURE OF ROOTS
(i) If b2 — 4ac > 0, then the roots are real and distinct.
(ii) If b2 — 4ac = 0, the roots are real and equal or coincident.
(iii) If b2 — 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 x2 — (α + β)x + αβ =0
Let α and β be two roots of the quadratic equation (ax2 + bx + c = 0 then
Sum of Roots: – the coefficient of x / the coefficient t of x2 ⇒ α + β = – b / a
Product of Roots :
αβ = constant term / the coefficient t of x2 ⇒ 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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