Question 1: Solve:

(i) (ii) (iii)

Answer:

(i)

(ii)

(iii)

Answer:

Question 3: Find the quadratic equation whose solution set is {-2, 3}.

Answer:

Since, solution set

which is the required quadratic equation.

Question 4: Use the substitution to solve for , if

Answer:

Question 5: Without solving the quadratic equation find whether is a solution (root) of this equation or not.

Answer:

Substituting in the given equation we get :

Which is true.

Therefore is a solution of the given equation

Question 6: Without solving the quadratic equation find whether is a solution (root) of this equation or not.

Answer:

Substituting in the given equation we get :

Which is not true.

Therefore is a solution of the given equation

Question 7: Find the value of for which is a root (solution) of equation

Answer:

Substituting in the given equation we get :

Question 8: If and are roots of the equation find the values of and

Answer:

is a root of the equation

is a root of the equation

On solving equations I and II, we get and

Question 9: If one root of the quadratic equation is 2 , find the value of Also, find the other root.

Answer:

Since, is a root of the given equation

Substituting we get :

Question 10: Solve each of the following equations by using the formula:

(i) (ii) (iii)

Answer:

Substituting the values we get

Substituting the values we get

Substituting the values we get

Question 11: Witt out solving, examine the nature of the roots of the equations :

(i) (ii) (iii)

Answer:

Therefore Discriminant which is negative.

Therefore the roots are not real i.e the roots are imaginary.

Therefore Discriminant

Therefore the roots are equal.

Therefore Discriminant which is positive.

Therefore the roots are real and unequal.

Question 12: Find the value of is the roots of the following quadratic equation are equal:

Answer:

Since the roots are equal, the discriminant is

Question 13: Find the value of is the roots of the following quadratic equation are equal:

Answer:

Since the roots are equal, the discriminant is

Therefore or

Question 14: Solve each of the following equations for x and give, in each case, your answer correct to 2 decimal places.

(i) (ii)

Answer:

or correct to 2 decimal places:

or correct to 2 decimal places:

Give your answer correct to two significant figures. [ICSE Board 2011]

Answer:

Substituting the values we get

or correct to 2 decimal places:

Question 16: Solve:

(i) (ii)

Answer:

(i)

Let Substituting:

(ii)

Let Substituting:

Answer:

Therefore Given equation reduces to:

Question 18: Find the solution set of the equation when

(i) (integers) (ii) ( Rational Numbers)

Answer:

Question 19: Solve:

Answer:

Answer:

Answer: