CLASS-10

BOARD: CBSE

Mathematic Worksheet - 4

TOPIC: Quadratic Equation

For other **CBSE Worksheet for class 10 Mathematic** check out main page of Entrancei.

__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

i.b=0 ,c ≠0 i.e of the type ax^{2} + c=0

ii.b ≠0 ,c=0 i.e of the type ax^{2} +bx=0

iii. b 0 ,c 0 i.e of the type ax^{2}=0

iv. 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)

Thenα=(-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=**

a) 0

b) 5

c) 1/6

d) 6

**2) The root of the equation x ^{2}-x-3=0 are**

a) Imaginary

b) Rational

c) irrational

d) none of these

**3) The difference between two numbers is 5 and the difference of their squares is 65.The larger number is**

a) 9

b) 10

c) 11

d) 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**

a) 30yrs

b) 31yrs

c) 36yrs

d) 41yrs.

**5) If one of the roots of the quadratic equation is 2 + then find the quadratic equation**

a) x^{2}-(2 + √3)x+1=0

b) x^{2}+(2 +√3)x+1=0

c) x^{2}-4x+1=0

d) x^{2}+4x-1=0

**Subjective**

**1) Find the value of k for which quadratic equation (k-2)x ^{2} +2(2k-3)x + 5k-6=0 has equal roots.**

**2) The length of a right triangle are %x +2,5x and 3x-1.If x>0 find the length of each side.**

**3) 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.**

**4) Solve the quadratic equation (x-1)/(x-2)-(x-2)/(x-3)=(x-5)/(x-6)-(x-6)/(x-7)**

**5) Solve the following equation for x**

9x^{2}-9(a + b) x+(2a^{2}+5ab+2b^{2}) = 0

**6) 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: **

1) b

2) c

3) a

4) c

5) c

**Subjective: **

1) k =3 or 1

2)17,15,8

3) 3/4

4) 9/2

5) 2a+b/3 , a+2b/3

6) 6 yrs, 12 yrs