Chapter 5 - Quadratic Equations Exercise Ex. 5(C)

Question 1

Solve : 

Solution 1

Question 2

Solve : 

Solution 2

Question 3

Solve : 

Solution 3

Question 4

Solve : 

Solution 4

Question 5

Solve : 

Solution 5

Question 6

Solve : 

Solution 6

Question 7

Solve : 

Solution 7

Question 8

Solve : 

Solution 8

Question 9

Solve : 

Solution 9

Question 10

Solve : 

Solution 10

Question 11

Solve : 

Solution 11

Question 12

Solve : 

Solution 12

Question 13

Solve : 

Solution 13

Question 14

Solve : 

Solution 14

Question 15

Solve : 

Solution 15

Question 16

2x² - 9x + 10 = 0, When

(i) x∈ N

(ii) x∈ Q

Solution 16

Question 17

Solve : 

Solution 17

Question 18

Solve : 

Solution 18

Question 19

Solve : 

Solution 19

Question 20

Solve : 

Solution 20

Question 21

Find the quadratic equation, whose solution set is :

(i) (ii)

Solution 21

Question 22(i)

 

Solution 22(i)

Question 22(ii)

 

Solution 22(ii)

Question 23

Find the value of x, if a + 1=0 and x² + ax - 6 =0.

Solution 23

If a+1=0, then a = -1

Put this value in the given equation x² + ax - 6 =0

Question 24

Find the value of x, if a + 7=0; b + 10=0 and 12x² = ax - b.

Solution 24

If a + 7 =0, then a = -7

and b + 10 =0, then b = - 10

 

Put these values of a and b in the given equation

Question 25

Use the substitution y= 2x +3 to solve for x, if 4(2x+3)² - (2x+3) - 14 =0.

Solution 25

4(2x+3)² - (2x+3) - 14 =0

Put 2x+3 = y

Question 26

Without solving the quadratic equation 6x² - x - 2=0, find whether  is a solution of this equation or not.

Solution 26

Consider the equation, 6x² - x - 2=0

Put  in L.H.S.

Since L.H.S.= R.H.S., then  is a solution of the given equation.

Question 27

Determine whether x = -1 is a root of the equation x² - 3x +2=0 or not.

Solution 27

x² - 3x +2=0

Put x = -1 in L.H.S.

L.H.S. = (-1)² - 3(-1) +2

= 1 +3 +2=6 R.H.S.

Then x = -1 is not the solution of the given equation.

Question 28

If x = is a solution of the quadratic equation 7x²+mx - 3=0;

Find the value of m.

Solution 28

7x²+mx - 3=0

Given x =  is the solution of the given equation.

Put given value of x in the given equation

Question 29

If x = -3 and x =  are solutions of quadratic equation mx² + 7x + n = 0, find the values of m and n.

Solution 29

Question 30

If quadratic equation x² - (m + 1) x + 6=0 has one root as x =3;

find the value of m and the root of the equation.

Solution 30

Question 31

Given that 2 is a root of the equation 3x² - p(x + 1) = 0 and that the equation px² - qx + 9 = 0 has equal roots, find the values of p and q.

Solution 31

Question 32

Solution 32

or x = -(a + b)

Question 33

Solution 33

Question 34

If -1 and 3 are the roots of x²+px+q=0
then find the values of p and q

Solution 34