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Title: Number system
Description: I am explaining number system upto 10th class chapter 1 number system
Description: I am explaining number system upto 10th class chapter 1 number system
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Maths Class 10 Notes for Quadratic Equations
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
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There are two types of quadratic equation
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SOLUTION OF A QUADRATIC EQUATION BY
FACTORISATION
A real number x is called a root of the quadratic equation ax2 + bx + c =0, a 0 if aα2 + bα + c
=0
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NOTE:
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2
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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
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DISCRIMINANT
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The expression b2 — 4ac is called the discriminant of the quadratic equation
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Find D = b2 — 4ac
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(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
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ROOTS OF THE QUADRATIC EQUATION
Let the quadratic equation be ax2 + bx + c = 0 (a ≠ 0)
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NATURE OF ROOTS
(i) If b2 — 4ac > 0, then the roots are real and distinct
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(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 x 2 —
(α + β)x + αβ =0
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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
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ncerthelp
Title: Number system
Description: I am explaining number system upto 10th class chapter 1 number system
Description: I am explaining number system upto 10th class chapter 1 number system