CBSE Worksheet for chapter-4 Quadratic Equation class 10
Worksheet For class 10
Find CBSE Worksheet for chapter- 4 Quadratic Equation class 10
CLASS-10
BOARD: CBSE
Mathematic Worksheet - 4
TOPIC: Quadratic Equation
For other CBSE Worksheet for class 10 Mathematic check out main page of Physics Wallah.
SUMMARY
GENERAL FORM OF QUADRATIC EQUATION:
The general form of quadratic equation is ax^{2} + bx + c where a, b, c are real numbers and a ≠ 0.
Since a Quadratic equations In general are of the following types
- b = 0 ,c ≠ 0 i.e of the type ax^{2} + c = 0
- b ≠ 0 ,c = 0 i.e of the type ax^{2} +bx = 0
- b 0 ,c 0 i.e of the type ax^{2} = 0
- b ≠ 0 ,c ≠ 0 i.e of the type ax^{2} + bx +c = 0
ROOTS OF A QUADRATIC EQUATION
The value of x which satisfies the given equation is known as its root .The roots of a given equation are known as it solution.
NATURE OF THE ROOTS
Let the root of the quadratic equation ax^{2} +by +c = 0(where a 0,b,c€ R)
Then α = (-b+√(b^{2}-4ac))/2a ;β = (-b-√(b^{2}-4ac))/2a
The nature of the roots depends upon the value of expression within the square root sign. This is known as discriminant of the given quadratic equation.
OBJECTIVE
1 ) If one of the root of 5x^{2} +13x + k = 0 is reciprocal of the other then k=
- 0
- 5
- 1/6
- 6
2) The root of the equation x^{2} - x - 3 = 0 are
- Imaginary
- Rational
- irrational
- none of these
3) The difference between two numbers is 5 and the difference of their squares is 65.The larger number is
- 9
- 10
- 11
- 12
4) The sum of the ages of father and the son is 45 yrs. Five years ago, the product of their age was 4 times the age of the father at that time. The present age of the father is
- 30yrs
- 31yrs
- 36yrs
- 41yrs
5) If one of the roots of the quadratic equation is 2 + then find the quadratic equation
- x^{2} - (2 + √3)x + 1 = 0
- x^{2} + (2 +√3)x + 1=0
- x^{2 }- 4x + 1 = 0
- x^{2} + 4x - 1 = 0
Subjective
- Find the value of k for which quadratic equation (k - 2)x^{2} + 2(2k - 3)x + 5k - 6 = 0 has equal roots.
- The length of a right triangle are %x +2,5x and 3x-1.If x>0 find the length of each side.
- The numerator of a fraction is less than its denominator. If 3 is added to each of the numerator and denominator, the fraction is increased by 3/28.Find the fraction.
- Solve the quadratic equation (x - 1)/(x - 2) - (x - 2)/(x - 3) = (x - 5)/(x - 6) - (x - 6)/(x - 7)
- Solve the following equation for x 9x^{2} - 9(a + b) x + (2a^{2 }+ 5ab + 2b^{2}) = 0
- A girl twice as old as her sister Four years hence the product of their ages (in years) will be 160. Find their present ages
Answers:
Objective:
- b
- c
- a
- c
- c
Subjective:
- k =3 or 1
- 17,15,8
- 3/4
- 9/2
- 2a+b/3 , a+2b/3
- 6 yrs, 12 yrs
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