Chapter 4 Quadratic Equations- MCQ Online Test 1 Class 10 Maths
1. What is the quadratic equation whose one of the roots is 3?
a. x2 − 5x + 6 = 0
b. x2 − 6x + 6 = 0
c. 2x2 − 5x + 6 = 0
d. 3x2− 3x + 6 = 0
2. The product of two consecutive integers is 240. What is the quadratic representation of the above situation?
a. x+1 = 150
b. x(x+1) = 240
c. x(x+2) = 280
d. x + 4 = 130
3. Find the roots of a quadratic equation x2−4px+4p2−q2= 0?
a. x = 2p + q
b. x = 2p − q
c. Both a and b
d. None of these
4. If x = 2 is a root of the quadratic equation 3x2 – px – 2 = 0, then find the value of ‘p’?
a. 2
b. 5
c. 3
d. 1
5. The product of two consecutive integers is 370. Find the quadratic representation of the above situation?
a. x(x+1) = 200
b. x+1 = 150
c. x-1 = 100
d. x(x+1) = 370
6. If p = – 7 and q = 12 and x2+ px + q = 0, then Find the value of ‘x’?
a. 3
b. 4
c. Both a and b
d. None of these
7. Find the common root of 2x2 + x – 6 = 0 and x2 −3x – 10 = 0?
a. 5
b. 3
c. -2
d. -4
8. The product of two successive integral multiples of 5 is 1050. Find the numbers.
a. 30
b. 35
c. Both a and b
d. None of these
9. Rohan’s mother is 26 years older than him. The product of their ages 3 years from now will be 360, then find Rohan’s present age?
a. 7
b. 8
c. 10
d. 12
10. A rectangular field is 16m long and 10m wide. There is a path of uniform width all around it having an area of 120 sq.m, then find the width of the path?
a. 2m
b. 5m
c. 8m
d. 3m
Chapter - 4 Quadratic Equations Quiz-1 | Math Class 10th
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Question 1 of 10
1. Question
What is the quadratic equation whose one of the roots is 3?
Correct
Since 3 is root of the equation, x = 3 must satisfy the equation.
Applying x =3 in the equation x2 − 5x + 6 = 0
gives, (3)2− 5(3) + 6 = 0
9 −15 + 6 = 0
15 −15 = 0
0 = 0
L.H.S. = R.H.S.
Hence, x2 − 5x + 6 = 0 is a required equation which has 3 as root.Incorrect
Since 3 is root of the equation, x = 3 must satisfy the equation.
Applying x =3 in the equation x2 − 5x + 6 = 0
gives, (3)2− 5(3) + 6 = 0
9 −15 + 6 = 0
15 −15 = 0
0 = 0
L.H.S. = R.H.S.
Hence, x2 − 5x + 6 = 0 is a required equation which has 3 as root. -
Question 2 of 10
2. Question
The product of two consecutive integers is 240. What is the quadratic representation of the above situation?
Correct
Let one of the two consecutive integers be x then the other consecutive integer will be (x+1)
∴ According to question, (x) × (x+1) = 240
x (x+1) = 240
Incorrect
Let one of the two consecutive integers be x then the other consecutive integer will be (x+1)
∴ According to question, (x) × (x+1) = 240
x (x+1) = 240
-
Question 3 of 10
3. Question
Find the roots of a quadratic equation x2−4px+4p2−q2= 0?
Correct
x2 − 4px + 4p2 − q2 = 0
(x−2p)2 − q2 = 0
Using a2 – b2 = (a + b) (a-b)
(x−2p+q) (x−2p−q) = 0
x − 2p + q = 0 and x−2p−q=0
x = 2p − q and x = 2p + qIncorrect
x2 − 4px + 4p2 − q2 = 0
(x−2p)2 − q2 = 0
Using a2 – b2 = (a + b) (a-b)
(x−2p+q) (x−2p−q) = 0
x − 2p + q = 0 and x−2p−q=0
x = 2p − q and x = 2p + q -
Question 4 of 10
4. Question
If x = 2 is a root of the quadratic equation 3 x2 – p x – 2 = 0, then find the value of ‘p’?
Correct
Given: p(x) = 3 x2 – p x – 2 = 0
∴p (2) = 3(2)2 − p (2) – 2 = 0
12 − 2 p – 2 = 0
−2 p = −10
p = 5Incorrect
Given: p(x) = 3 x2 – p x – 2 = 0
∴p (2) = 3(2)2 − p (2) – 2 = 0
12 − 2 p – 2 = 0
−2 p = −10
p = 5 -
Question 5 of 10
5. Question
The product of two consecutive integers is 370. Find the quadratic representation of the above situation?
Correct
Let one of the two consecutive integers be x then the other consecutive integer will be (x+1).
∴ According to question, (x) × (x+1) = 370
x (x+1) = 370
Incorrect
Let one of the two consecutive integers be x then the other consecutive integer will be (x+1).
∴ According to question, (x) × (x+1) = 370
x (x+1) = 370
-
Question 6 of 10
6. Question
If p = – 7 and q = 12 and x2+ px + q = 0, then Find the value of ‘x’?
Correct
Putting the values of p and q in given equation, we get
x2+ (−7) x + 12 = 0
x2 −7x + 12 = 0
x2 −4x −3x + 12 = 0
x(x−4)−3(x−4) = 0
(x−3)(x−4) = 0
x – 3 = 0 and x−4 = 0
x = 3and x = 4Incorrect
Putting the values of p and q in given equation, we get
x2+ (−7) x + 12 = 0
x2 −7x + 12 = 0
x2 −4x −3x + 12 = 0
x(x−4)−3(x−4) = 0
(x−3)(x−4) = 0
x – 3 = 0 and x−4 = 0
x = 3and x = 4 -
Question 7 of 10
7. Question
Find the common root of 2x2 + x – 6 = 0 and x2 −3x – 10 = 0?
Correct
Given: Putting X= -2 in given equations
p(x) =2x2+x−6 = 0 and q(x) = x2−3x−10 = 0
∴p(−2) = 2(−2)2+(−2)−6 = 0= 8 – 2 – 6 = 8 – 8 = 0
∴q (−2) = (−2)2−3 (−2) −10 = 0= 4 + 6 – 10 = 10 – 10 = 0
since p (−2) =0 and q (−2) =0
Therefore, −2 is the common root of 2x2+x−6 = 0 and x2−3x−10 = 0Incorrect
Given: Putting X= -2 in given equations
p(x) =2x2+x−6 = 0 and q(x) = x2−3x−10 = 0
∴p(−2) = 2(−2)2+(−2)−6 = 0= 8 – 2 – 6 = 8 – 8 = 0
∴q (−2) = (−2)2−3 (−2) −10 = 0= 4 + 6 – 10 = 10 – 10 = 0
since p (−2) =0 and q (−2) =0
Therefore, −2 is the common root of 2x2+x−6 = 0 and x2−3x−10 = 0 -
Question 8 of 10
8. Question
The product of two successive integral multiples of 5 is 1050. Find the numbers.
Correct
Let one multiple of 5 be x then the next consecutive multiple of will be (x+5)
According to question,
x(x+5) =1050
x2+5x−1050 = 0
x2+35x−30x−1050 = 0
x(x+35)−30(x+35) = 0
(x−30)(x+35) = 0
x−30 = 0 and x+35 = 0
x = 30 and x = −35
x = −35 is not possible therefore x = 30
Then the other multiple of 5 is x+5 = 30 + 5 = 35
Then the number are 30 and 35.Incorrect
Let one multiple of 5 be x then the next consecutive multiple of will be (x+5)
According to question,
x(x+5) =1050
x2+5x−1050 = 0
x2+35x−30x−1050 = 0
x(x+35)−30(x+35) = 0
(x−30)(x+35) = 0
x−30 = 0 and x+35 = 0
x = 30 and x = −35
x = −35 is not possible therefore x = 30
Then the other multiple of 5 is x+5 = 30 + 5 = 35
Then the number are 30 and 35. -
Question 9 of 10
9. Question
Rohan’s mother is 26 years older than him. The product of their ages 3 years from now will be 360, then find Rohan’s present age?
Correct
Let Rohan’s present age be x years.
Then Rohan’s mother age will be (x+26) years.
And after 3 years their ages will be (x+3) and (x+29) years.
According to question,
(x+3)(x+29) = 360
x2 + 29 x + 3 x+87 = 360
x2 + 32 x−273 = 0
x2 + 39 x−7 x−273 = 0
x(x+39)−7(x+39) = 0
(x−7)(x+39) = 0
x−7 = 0 and x+39 = 0
x = 7 and x = −39 [x = −39 is not possible]
Therefore, Rohan’s present age is 7 years.Incorrect
Let Rohan’s present age be x years.
Then Rohan’s mother age will be (x+26) years.
And after 3 years their ages will be (x+3) and (x+29) years.
According to question,
(x+3)(x+29) = 360
x2 + 29 x + 3 x+87 = 360
x2 + 32 x−273 = 0
x2 + 39 x−7 x−273 = 0
x(x+39)−7(x+39) = 0
(x−7)(x+39) = 0
x−7 = 0 and x+39 = 0
x = 7 and x = −39 [x = −39 is not possible]
Therefore, Rohan’s present age is 7 years. -
Question 10 of 10
10. Question
A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it having an area of 120 sq.m, then find the width of the path?
Correct
Let width of the path be x m
∴ Area of path = Area of ABCD – Area of PQRS
120 = (16+2x)(10+2x)−16×10
120 = 160 + 32x + 20x + 4x2−160m
4 x2+ 52 x−120 = 0
x2+ 13 x−30 = 0
x2+ 15 x−2 x−30 = 0
x(x+15)−2(x+15) = 0
(x+15)(x−2) = 0
x+15=0 and x−2 = 0
x = −15 and x = 2 [x=−15 is not possible]
Therefore, the width of the path is 2 m.Incorrect
Let width of the path be x m
∴ Area of path = Area of ABCD – Area of PQRS
120 = (16+2x)(10+2x)−16×10
120 = 160 + 32x + 20x + 4x2−160m
4 x2+ 52 x−120 = 0
x2+ 13 x−30 = 0
x2+ 15 x−2 x−30 = 0
x(x+15)−2(x+15) = 0
(x+15)(x−2) = 0
x+15=0 and x−2 = 0
x = −15 and x = 2 [x=−15 is not possible]
Therefore, the width of the path is 2 m.