Quadratic equations for class 10
Quadratic equations
In this you have to study about quadratic equation and its quadratic equation concept like quadratic expression , quadratic equations for class 10 , quadratic equations 10th class , quadratic equations of class 10 , quadratic equations how to solve , solving for quadratic equations , identity , discriminant , polynomial and many other that are mentioned below. If you find errors then tell me in comment section and don't forget to subscribe our page by your email.
Quadratic equation class 10
What is Quadratic Equation ?
We know that the square root of a negative real number is known as imaginary number. We have also seen in carlier classes that roots of the quadratic equation
ax² + bx +c=0 are given by
Quadratic equation root formula
Quadratic equation notes
b² - 4ac is called the discriminant of the quadratic equation ax² +bx+c= 0 and is denoted by D.
If b² < 4ac is, D<0 then D will be an imaginary number and if a, b.c are real numbers, then roots of the quadratic equation will be imaginary
HOW to solve quadratic equations
SOME DEFINITIONS
Equation : An equation is an equality which is satisfied only by some particular values of the variables occurring in it.
Quadratic equation : An equation of the form ax² + bx+c=0, where a,b,c are certain numbers, and a is not equal to 0 is called a quadratic equation
The numbers a, b,c are called the coefficients of the quadratic equation and the number b² - 4ac is called its discriminant
Discriminant of a quadratic equation is usually denoted by D or A.
Quadratic equation example :
(i) 3x² + 2x -1=0 is a quadratic equation
Here a = 3, b = 2, c=-1
(ii) 2 x³+5=0 is not a quadratic equation
(iii) 2x² -x¹/² + 3= 0 is not a quadratic equation
The quadratic equation ax +dx+e 0 is called incomplete if at least one of the coefficients b or e is zero.
EXAMPLE: 2x² + 5 = 0 is an incomplete quadratic equation.
What is quadratic expression
Quadratic Expression: An expression of the form ax² + bx +c, where
a, b.c are some numbers and a not equal to 0 is called a quadratic expression
What is identity
Identity : If two expressions in x are equal for all values of x. This statement of equality between the two expressions is called an identity
Another definition: f(x) is said to be an identity in x if it is satisfied by Thus an identity in x is satisfied by all values of r whereas an equation in is satisfied by some particular values of x
EXAMPLE (x+1)² = x²+2x+1 is an identity in x.
Here highest power of x in the given relation is 2 and this relation is satisfied by three different values x = 0, x = 1 and x = -1. Hence it is an identity because a polynomial equation of th degree cannot have more than n distinct roots.
(ii) 2x⁹⁰ -x⁷ +5=0 is an equation in x because it is not satisfied by x = 0 The symbol = is used to identify an identity from an equation
Note: In an identity in x coefficients of similar powers of x on the two sides are equal Thus
if ax³ + bx² +cx+d = 7x³ - 5x² + 8x - 6 be an identity in x then a = 7 b=-- 5.c = 8, d = -6
What is identical equations ?
Identical equations : Two equations are said to be identical if they have same roots.
EXAMPLE : x² - 5x+4 = 0 and 2x² - 10x + 8=0 are identical equations because both these equations have same roots 1 and 4.
Note: (1) Two equations in x are identical if and only if the coefficients of similar power of x in the two equations are proportional. Thus if ax² + bx+c 0 and ax² +bx+c =0 are identical equations
(2) An equation remains unchanged if it is multiplied or divided by a non-zero number
6. Polynomial : An expression of the form
a₀xⁿ +a₁xⁿ⁻¹ +a₂xⁿ⁻² -------- aₙ⁻₁x + aₙ
polynomial in x of degree n. As a special case a constant is also called a polynomial of degree zero.
EXAMPLE (1) 3x² - 5x+7 is a polynomial of degree 2.
Quadratic equation have only two roots
Quadratic equation roots | quadratic equation formula for roots
Quadratic equation with real co-efficient
Type 1
In the following equations solve by using the factorization method
1. 2x +3=0
2. x - 4x + 7 = 0
3. 9x - 12x + 20 = 0
4. x +2x + 5=0
Type II
In the following equations solve by using the general expression for roots of quadratic equation:
5. 2x² - 3x +1=0
6. 5x² - 6x + 2 = 0
7. 8x² - 9x + 3=0
8. x² -x+1=0
9. 27x² +10x+1=0
10. x² +x+1=0
11. X² +3=0
12. 27x² - 10x + 1 = 0
13. 17x² - 8x+1=0
14. 32x² - 7x +5=0
15. 9x² +4x =0
16. x² - 4x +7=0
17. x² + 2x +2=0
18. x² + 3x +9=0
19. x² +3x +5=0
20. 21x² +x+1=0
21. x² +x+1=0
22.4x² - 4x+ 13 =0
23. x² +2x + 5=0
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