QUADRATIC EQUATIONS
QUADRATIC EQUATION
1) For each of the following, determine whether the given equations have root(s). If so find the root(s)
i) √7y^2 – 6y -13√7=0
ii) (x+4) (x+5) = 3(x+1) (x+2) + 2x
iii) 1/x+1 + 2/x+2 = 4/x+4
2) In each of the following, determine value(s) for which the given equation has real roots:-
i) 5px^2 - 8x +1 =0
ii) 4x^^2 + 8x – p =0
iii) 4x2 – 3px + 9=0
3) Solve
i) abx^2 + (b^2-ac)x –bc =0
ii) x-1/x-2 + x-3/x-4 = 10/3
iii) x+1/x-1 + x-2/x+2 = 3
4) Divide 12 into 2 parts such that their product is 32.
[ans. 4 or 8]
5) Divide 12 into 2 parts such that the sum of their square is 74.
[ans. 5 or 7]
6) The sum of a no. and its reciprocal is 10/3. Find the no.
[ans. 3 or 1/3]
7) The denominator of a fraction is one more than twice the numerator. If the
sum of the fraction and its reciprocal is 58/21. Find the fraction.
[ans. 3/7]
8) The product of Ramu’s age 5 yrs ago and his age 9 yrs later is 15. Determine
Ramu’s age.
[ans. 6 yrs]
9) There are 3 consecutive +ve integers such that the sum of the square of the first
and the product of the other 3 is 154. What are the integers?
[ans. 20, 21, 22]
10) The sum of the ages of a father and hid son is 45 yrs. 5
yrs ago, the product of their ages was 124. Determine
their present ages.
[ans. 18 yrs and 27 yrs]
11) A passenger train takes 2 hrs less for a journey of 300 km, if its speed is increased
by 5 km/hr from the usual speed. Find its usual speed.
[ans. 25 km/hr]
12) Vikram wishes to fit 3 rods together in the shape of a right triangle. The
hypotenuse is to be 2 cm longer than the base and 4 cm longer than the altitude.
What should be the lengths of the rods.
[ans. 10 cm, 8 cm, 6 cm]
13) A motor boat, whose speed is 15 km/hr in still water, goes 30 km downstream and
comes back in a total time of 4 hrs 30 mins. Find the speed of the stream.
[ans. 5 km/hr]
14) A journey of 192 km from Mumbai to pune takes 2 hr less by a super fast train
than by an ordinary train. If the average speed of the slower train is 16 km/hr less
than that of the faster train. Determine their average speeds.
[ans. 32 km/hr and 48 km/hr]
15) A farmer wishes to grow a 100sq. m rectangular vegetable garden. Since he has
with him only 30 m barbed wire, he fences 3 sides of his garden letting compound
wall of his house act as a fourth side fence. Find the dimensions of his garden.
[ans. 10 x 10 or 5 x 20]
16) The sum S of n successive odd natural nos. starting from 3 is given by the
relation S=n (n+2). Determine n, if the sum is 168.
[ans. 12]
17) Some students arranged a picnic. The budget for food was Rs.240. Because 4
students of the group failed to go, the cost of food to each student got increased by
Rs.5. How many students went for the picnic?
[ans. 12]
18) If a student had walked 1km/hr faster, he would have taken 15 mins less to walk 3
km. Find the rate at which he was walking.
[ans. 3 km/hr]
19) Sum of the area of 2 squares is 468 sq.m. If the difference of their perimeter is
24m, find the sides of the 2 squares.
[ans. 18 m and 12 m]
20) A fast train takes 3 hrs less than a slow train for a journey of 600 km. If the speed
of the slow train is 10 km/hr less than that of the fast train, find the speed of the 2
train.
[ans. 40 km/hr and 50 km/hr]
Made by:
Nitika Rattan
1) For each of the following, determine whether the given equations have root(s). If so find the root(s)
i) √7y^2 – 6y -13√7=0
ii) (x+4) (x+5) = 3(x+1) (x+2) + 2x
iii) 1/x+1 + 2/x+2 = 4/x+4
2) In each of the following, determine value(s) for which the given equation has real roots:-
i) 5px^2 - 8x +1 =0
ii) 4x^^2 + 8x – p =0
iii) 4x2 – 3px + 9=0
3) Solve
i) abx^2 + (b^2-ac)x –bc =0
ii) x-1/x-2 + x-3/x-4 = 10/3
iii) x+1/x-1 + x-2/x+2 = 3
4) Divide 12 into 2 parts such that their product is 32.
[ans. 4 or 8]
5) Divide 12 into 2 parts such that the sum of their square is 74.
[ans. 5 or 7]
6) The sum of a no. and its reciprocal is 10/3. Find the no.
[ans. 3 or 1/3]
7) The denominator of a fraction is one more than twice the numerator. If the
sum of the fraction and its reciprocal is 58/21. Find the fraction.
[ans. 3/7]
8) The product of Ramu’s age 5 yrs ago and his age 9 yrs later is 15. Determine
Ramu’s age.
[ans. 6 yrs]
9) There are 3 consecutive +ve integers such that the sum of the square of the first
and the product of the other 3 is 154. What are the integers?
[ans. 20, 21, 22]
10) The sum of the ages of a father and hid son is 45 yrs. 5
yrs ago, the product of their ages was 124. Determine
their present ages.
[ans. 18 yrs and 27 yrs]
11) A passenger train takes 2 hrs less for a journey of 300 km, if its speed is increased
by 5 km/hr from the usual speed. Find its usual speed.
[ans. 25 km/hr]
12) Vikram wishes to fit 3 rods together in the shape of a right triangle. The
hypotenuse is to be 2 cm longer than the base and 4 cm longer than the altitude.
What should be the lengths of the rods.
[ans. 10 cm, 8 cm, 6 cm]
13) A motor boat, whose speed is 15 km/hr in still water, goes 30 km downstream and
comes back in a total time of 4 hrs 30 mins. Find the speed of the stream.
[ans. 5 km/hr]
14) A journey of 192 km from Mumbai to pune takes 2 hr less by a super fast train
than by an ordinary train. If the average speed of the slower train is 16 km/hr less
than that of the faster train. Determine their average speeds.
[ans. 32 km/hr and 48 km/hr]
15) A farmer wishes to grow a 100sq. m rectangular vegetable garden. Since he has
with him only 30 m barbed wire, he fences 3 sides of his garden letting compound
wall of his house act as a fourth side fence. Find the dimensions of his garden.
[ans. 10 x 10 or 5 x 20]
16) The sum S of n successive odd natural nos. starting from 3 is given by the
relation S=n (n+2). Determine n, if the sum is 168.
[ans. 12]
17) Some students arranged a picnic. The budget for food was Rs.240. Because 4
students of the group failed to go, the cost of food to each student got increased by
Rs.5. How many students went for the picnic?
[ans. 12]
18) If a student had walked 1km/hr faster, he would have taken 15 mins less to walk 3
km. Find the rate at which he was walking.
[ans. 3 km/hr]
19) Sum of the area of 2 squares is 468 sq.m. If the difference of their perimeter is
24m, find the sides of the 2 squares.
[ans. 18 m and 12 m]
20) A fast train takes 3 hrs less than a slow train for a journey of 600 km. If the speed
of the slow train is 10 km/hr less than that of the fast train, find the speed of the 2
train.
[ans. 40 km/hr and 50 km/hr]
Made by:
Nitika Rattan
