If the graph of a polynomial intersects the x – axis at three points, then the number of zeroes will be
a) 0
b) at least three
c) at most three
d) 3
2. If ‘α’ and ‘β’ are the zeroes of a quadratic polynomial x^{2}+ 5x − 5, then
a) α + β = αβ
b) α + β > αβ
c) α + β < αβ
d) α − β = αβ
3. If one zero of the quadratic polynomial x^{2}+ 3x + k is 2, then the value of ‘k’ is
a) –5
b) –10
c) 10
d) 5
4. If x^{3}+x^{2}−2x−3=(x−2)(x^{2}+ax+b)+5, then
a) a = 5 and b = 6
b) a = 4 and b = 5
c) a = 3 and b = 4
d) a = – 3 and b = – 4
5. If √2 and –√2 are the zeroes of 2x^{4}−3x^{3}−3x^{2}+6x−2, then the other zeroes are
a) 2 and 1/2
b) 2 and –2
c) 1/2 and –1/2
d) –2 and –1/2
6. A polynomial of degree ____ is called a quadratic polynomial.
a) 1
b) 2
c) 0
d) 3
7. A polynomial of degree ‘n’ has
a) ‘n’ zeroes
b) at most ‘n’ zeroes
c) one zero
d) at least ‘n’ zeroes
8. If one zero of the polynomial p(x)=(k+4)x^{2}+13x+3k is reciprocal of the other, then the value of ‘k’ is
a) 4
b) 3
c) 2
d) 5
9. If one of the zeroes of the cubic polynomial x^{3}−7x+6 is 2, then the product of the other two zeroes is
a) –2
b) 3
c) –3
d) 2
10. If ‘2’ is the zero of both the polynomials 3x^{2} + mx − 14 and 2x^{3} + nx^{2} + x − 2, then the value of m – 2n is
a) –9
b) 9
c) –1
d) 5
Polynomial Chapter  2 Quiz 1 Class 10th
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Question 1 of 10
1. Question
If the graph of a polynomial intersects the x – axis at three points, then the number of zeroes will be
Correct
If the graph of a polynomial intersects the xaxis at three points, then the number of zeroes are 3 because the x axis is intersect three times by the three coordinates so,
number of zeroes of the polynomial = number of the coordinates of the points (where its graph intersects the xaxis.)Incorrect
If the graph of a polynomial intersects the xaxis at three points, then the number of zeroes are 3 because the x axis is intersect three times by the three coordinates so,
number of zeroes of the polynomial = number of the coordinates of the points (where its graph intersects the xaxis.) 
Question 2 of 10
2. Question
If ‘α’ and ‘β’ are the zeroes of a quadratic polynomial x^{2}+ 5x − 5, then
Correct
α+β=−b/a=−5/1 and αβ=c/a=−5/1
∴α+β=αβIncorrect
α+β=−b/a=−5/1 and αβ=c/a=−5/1
∴α+β=αβ 
Question 3 of 10
3. Question
If one zero of the quadratic polynomial x^{2}+ 3x + k is 2, then the value of ‘k’ is
Correct
Given Polynomial is p(x) = x^{2}+3x+k
According to question, p(x) = 0 (Put x = 2)
p(2) = 0
⇒(2)^{2}+(3×2)+k=0
⇒4+6+k=0
⇒k=−10Incorrect
Given Polynomial is p(x) = x^{2}+3x+k
According to question, p(x) = 0 (Put x = 2)
p(2) = 0
⇒(2)^{2}+(3×2)+k=0
⇒4+6+k=0
⇒k=−10 
Question 4 of 10
4. Question
If x^{3}+x^{2}−2x−3=(x−2)(x^{2}+ax+b)+5, then
Correct
Given: x^{3}+x^{2}−2x−3=(x−2)(x^{2}+ax+b)+5
Dividing L.H.S. by (x−2)
∴(x−2)(x^{2}+3x+4)+5=(x−2)(x^{2}+ax+b)+5
Comparing both side, we have a=3,b=4Incorrect
Given: x^{3}+x^{2}−2x−3=(x−2)(x^{2}+ax+b)+5
Dividing L.H.S. by (x−2)
∴(x−2)(x^{2}+3x+4)+5=(x−2)(x^{2}+ax+b)+5
Comparing both side, we have a=3,b=4 
Question 5 of 10
5. Question
If √2 and –√2 are the zeroes of 2x^{4}−3x^{3}−3x^{2}+6x−2, then the other zeroes are
Correct
Since √2 and –√2 are the zeroes of 2x^{4}−3x^{3}−3x^{2}+6x−2,
then(x−√2) and (x+√2) are the factors of given polynomial
(x−√2)(x+√2)=(x2−2) is a factor of given polynomial.
∴ p(x)= 2x^{4}−3x^{3}−3x^{2}+6x−2
⇒ p(x)=(x^{2}−2)(2x^{2}−3x+1)
⇒ p(x)=(x^{2}−2)[2x^{2}−2x−x+1]
⇒ p(x)=(x^{2}−2)[2x(x−1)−1(x−1)]
⇒ p(x)=(x^{2}−2)(x−1)(2x−1)
∴ Other zeroes are x−1=0 and 2x−1=0
⇒x=1 and x=1/2Incorrect
Since √2 and –√2 are the zeroes of 2x^{4}−3x^{3}−3x^{2}+6x−2,
then(x−√2) and (x+√2) are the factors of given polynomial
(x−√2)(x+√2)=(x2−2) is a factor of given polynomial.
∴ p(x)= 2x^{4}−3x^{3}−3x^{2}+6x−2
⇒ p(x)=(x^{2}−2)(2x^{2}−3x+1)
⇒ p(x)=(x^{2}−2)[2x^{2}−2x−x+1]
⇒ p(x)=(x^{2}−2)[2x(x−1)−1(x−1)]
⇒ p(x)=(x^{2}−2)(x−1)(2x−1)
∴ Other zeroes are x−1=0 and 2x−1=0
⇒x=1 and x=1/2 
Question 6 of 10
6. Question
A polynomial of degree ____ is called a quadratic polynomial.
Correct
A polynomial of degree 2 is called a quadratic polynomial.
Incorrect
A polynomial of degree 2 is called a quadratic polynomial.

Question 7 of 10
7. Question
A polynomial of degree ‘n’ has
Correct
A polynomial of degree ‘n’ has at most ‘n’ zeroes because degree of a polynomial is equal to the zeroes of that polynomial only.
Incorrect
A polynomial of degree ‘n’ has at most ‘n’ zeroes because degree of a polynomial is equal to the zeroes of that polynomial only.

Question 8 of 10
8. Question
If one zero of the polynomial p(x)=(k+4)x^{2}+13x+3k is reciprocal of the other, then the value of ‘k’ is
Correct
Let one zero of the given polynomial be α
the other zero is reciprocal be 1/α
∵(Products of Roots) αβ=c/a
α×1/α = 3k/(k+4)
1 = 3k/(k+4)
k+4 = 3k (by cross multiplication)
4= 3kk
4= 2k
k=4/2
k=2Incorrect
Let one zero of the given polynomial be α
the other zero is reciprocal be 1/α
∵(Products of Roots) αβ=c/a
α×1/α = 3k/(k+4)
1 = 3k/(k+4)
k+4 = 3k (by cross multiplication)
4= 3kk
4= 2k
k=4/2
k=2 
Question 9 of 10
9. Question
If one of the zeroes of the cubic polynomial x^{3}−7x+6 is 2, then the product of the other two zeroes is
Correct
Let α,β,γ are the zeroes of the given polynomial.
Given: α=2
Since αβγ=−d/a
⇒2×βγ=−6/1
⇒βγ=−6/2=−3Incorrect
Let α,β,γ are the zeroes of the given polynomial.
Given: α=2
Since αβγ=−d/a
⇒2×βγ=−6/1
⇒βγ=−6/2=−3 
Question 10 of 10
10. Question
If ‘2’ is the zero of both the polynomials 3x^{2} + mx − 14 and 2x^{3} + nx^{2} + x − 2, then the value of m – 2n is
Correct
According to the question, p(2)=3×2+mx−14=0
⇒3(2)^{2} + m×^{2} – 14 = 0
⇒12+2m−14=0⇒m=1
Also p(2)=2x^{3}+nx^{2}+x−2=0
⇒2×(2)^{3}+n×(2)^{2}+2−2=0
⇒16+4n=0
⇒n=−4
∴m−2n=1−2×(−4)=1+8=9Incorrect
According to the question, p(2)=3×2+mx−14=0
⇒3(2)^{2} + m×^{2} – 14 = 0
⇒12+2m−14=0⇒m=1
Also p(2)=2x^{3}+nx^{2}+x−2=0
⇒2×(2)^{3}+n×(2)^{2}+2−2=0
⇒16+4n=0
⇒n=−4
∴m−2n=1−2×(−4)=1+8=9