Chapter 2 Polynomials- MCQ Online Test 2 Class 10 Maths
1. A quadratic polynomial whose product and sum of zeroes are 1/3 and √2 respectively is
a) 3x2+x−3√2
b) 3x2−3√2 x+1
c) 3x2−x+3√2
d) 3x2+ 3√2x +1
2. The zeroes of the quadratic polynomial x2+9x+20 are
a) –4 and 5
b) –4 and –5
c) 4 and –5
d) 4 and 5
3. The polynomial 9x2+6x+4 has
a) many real zeroes
b) no real zeroes
c) two real zeroes
d) one real zero
4. The degree of a constant polynomial is
a) 2
b) 0
c) 1
d) 3
5. A polynomial whose sum and product of zeroes are –4 and 3 is
a) x2+4x+3
b) x2−4x+3
c) none of these
d) x2−4x−3
6. The zeroes of a polynomial x2+5x+6x are
a) one positive and one negative
b) both negative
c) both positive
d) both equal
7. The largest power of ‘x’ in p(x) is the _________ of the polynomial.
a) degree
b) zero
c) root
d) solution
8. The number polynomials having zeroes as –2 and 5 is
a) 3
b) 1
c) more than 3
d) 2
9. Given that one of the zeroes of the cubic polynomial ax3+bx2+cx+d is zero, then the product of the other two zeroes is
a) −b/a
b) −c/a
c) c/a
d) b/a
10. The degree of the polynomial 5x3−3x2−x+√2 is
a) 0
b) 1
c) 2
d) 3
Polynomial Chapter - 2 Quiz 2 Class 10th
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Question 1 of 10
1. Question
A quadratic polynomial whose product and sum of zeroes are 1/3 and √2 respectively is
Correct
Given: α+β = −b/a =√2/1=−(−√2)/1=−(−3√2)/3
And αβ=c/a=1/3
On comparing, we get, a=3,b=−3√2,c=1
Putting these values in general form of a quadratic polynomial ax2+bx+c,
we have 3x2−3√2x+1Incorrect
Given: α+β = −b/a =√2/1=−(−√2)/1=−(−3√2)/3
And αβ=c/a=1/3
On comparing, we get, a=3,b=−3√2,c=1
Putting these values in general form of a quadratic polynomial ax2+bx+c,
we have 3x2−3√2x+1 -
Question 2 of 10
2. Question
The zeroes of the quadratic polynomial x2+9x+20 are
Correct
(x2+9x+20)=0
Splitting the middle term, we get
x2+5x+4x+20=0
= x(x+5)+4(x+5)=0
= (x+5)(x+4)=0
∴x+5=0 and x+4=0
⇒x=−5 and x=−4Incorrect
(x2+9x+20)=0
Splitting the middle term, we get
x2+5x+4x+20=0
= x(x+5)+4(x+5)=0
= (x+5)(x+4)=0
∴x+5=0 and x+4=0
⇒x=−5 and x=−4 -
Question 3 of 10
3. Question
The polynomial 9x2+6x+4 has
Correct
The polynomial 9x2+6x+4 has no real zeroes because it is not factorizing.
Incorrect
The polynomial 9x2+6x+4 has no real zeroes because it is not factorizing.
-
Question 4 of 10
4. Question
The degree of a constant polynomial is
Correct
The degree of a constant polynomial is 0. e.g. 5 = 5x0
Incorrect
The degree of a constant polynomial is 0. e.g. 5 = 5x0
-
Question 5 of 10
5. Question
A polynomial whose sum and product of zeroes are –4 and 3 is
Correct
x2– (Sum the Zeroes)x + (Product of Zeroes)
x2 – (-4)x + 3
= x2 + 4x + 3Incorrect
x2– (Sum the Zeroes)x + (Product of Zeroes)
x2 – (-4)x + 3
= x2 + 4x + 3 -
Question 6 of 10
6. Question
The zeroes of a polynomial x2+5x+6x are
Correct
x2+5x+6
= x2+3x+2x+6
= x(x+3)+2(x+3)
= (x+3)(x+2)
x+3=0 or x+2=0
⇒ x=−3 or x=−2Incorrect
x2+5x+6
= x2+3x+2x+6
= x(x+3)+2(x+3)
= (x+3)(x+2)
x+3=0 or x+2=0
⇒ x=−3 or x=−2 -
Question 7 of 10
7. Question
The largest power of ‘x’ in p(x) is the _________ of the polynomial.
Correct
The largest power of ‘x’ in p(x) is the degree of the polynomial.
Incorrect
The largest power of ‘x’ in p(x) is the degree of the polynomial.
-
Question 8 of 10
8. Question
The number polynomials having zeroes as –2 and 5 is
Correct
The number polynomials having zeroes as –2 and 5 is more than 3.
If ‘S’ is the sum and ‘P’ is the product of the zeroes then the corresponding family of quadratic polynomial is given by
p(x)=k(x2−Sx+P)where k is any real number.
Therefore putting different values of k, we can make more than 3 numbers of polynomials.Incorrect
The number polynomials having zeroes as –2 and 5 is more than 3.
If ‘S’ is the sum and ‘P’ is the product of the zeroes then the corresponding family of quadratic polynomial is given by
p(x)=k(x2−Sx+P)where k is any real number.
Therefore putting different values of k, we can make more than 3 numbers of polynomials. -
Question 9 of 10
9. Question
Given that one of the zeroes of the cubic polynomial ax
Correct
Let α,β,γ are the zeroes of the given polynomial. Given : α=0
To find: βγ
Since, αβ+βγ+γα=c/a
∴0×β + βγ + γ × 0 =c/a ⇒βγ=c/aIncorrect
Let α,β,γ are the zeroes of the given polynomial. Given : α=0
To find: βγ
Since, αβ+βγ+γα=c/a
∴0×β + βγ + γ × 0 =c/a ⇒βγ=c/a -
Question 10 of 10
10. Question
The degree of the polynomial 5x3−3x2−x+√2 is
Correct
The degree of the polynomial 5x3−3x2−x+√2 is 3.
The degree of a polynomial is the highest power of that polynomial.Incorrect
The degree of the polynomial 5x3−3x2−x+√2 is 3.
The degree of a polynomial is the highest power of that polynomial.