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: