1. The degree of a biquadratic polynomial is
a) 2
b) 4
c) 3
d) 1
2. The zeroes of a polynomial x^{2}+5x+6 are
a) one positive and one negative
b) both negative
c) both positive
d) both equal
3. The number of zeroes that the polynomial f(x) = (x–2)^{2} + 4 can have is
a) 2
b) 3
c) 0
d) 1
4. The zeroes of a polynomial x^{2}+5x−24 are
a) both positive
b) one positive and one negative
c) both negative
d) both equal
5. The zeroes of a polynomial x^{2}−7x+12 are
a) both positive
b) one positive and one negative
c) both negative
d) both equal
6. A real number ‘k’ is said to be a zero of a polynomial p(x), if p(k) =
a) 2
b) 1
c) 3
d) 0
7. The zeroes of a polynomial x^{2}+4x+4 are
a) one positive and one negative
b) both negative
c) both equal
d) both positive
8. If the zeroes of a quadratic polynomial ax^{2} + bx + c, c ≠ 0 are equal, then
a) b and c have the same sign
b) b and c have opposite sign
c) c and a have opposite sign
d) c and a have the same sign
9. If a real number ‘α ’ is a zero of a polynomial, then ______ is a factor of f(x).
a) x−α
b) X±α
c) x+α
d) none of these
10. If ‘α’ and ‘β’ are the zeroes of a quadratic polynomial ax^{2}+bx+c, then α β =
a) −c/a
b) −b/a
c) b/a
d) c/a
Polynomial Chapter  2 Quiz 3 Class 10th
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Question 1 of 10
1. Question
The degree of a biquadratic polynomial is
Correct
Biquadratic polynomial = a(x^{2})^{2}+b(x)^{2}+c = ax^{4}+bx^{2}+c
Incorrect
Biquadratic polynomial = a(x^{2})^{2}+b(x)^{2}+c = ax^{4}+bx^{2}+c

Question 2 of 10
2. Question
The zeroes of a polynomial x^{2}+5x+6 are
Correct
x^{2}+5x+6
= x^{2}+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
x^{2}+5x+6
= x^{2}+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 3 of 10
3. Question
The number of zeroes that the polynomial f(x) = (x–2)^{2} + 4 can have is
Correct
f(x)=(x−2)^{2}+4+4
= x^{2}−4x+4+4
= x^{2}−4x+8
Here the largest exponent of variable is 2,
therefore number of zeroes of the given polynomial is 2.Incorrect
f(x)=(x−2)^{2}+4+4
= x^{2}−4x+4+4
= x^{2}−4x+8
Here the largest exponent of variable is 2,
therefore number of zeroes of the given polynomial is 2. 
Question 4 of 10
4. Question
The zeroes of a polynomial x^{2}+5x−24 are
Correct
x^{2}+5x−24
= x^{2}+8x−3x−24
= x(x+8)−3(x+8) = 0
(x+8)(x−3) = 0
∴x+8=0 or x−3=0
⇒x=−8 or x=3Incorrect
x^{2}+5x−24
= x^{2}+8x−3x−24
= x(x+8)−3(x+8) = 0
(x+8)(x−3) = 0
∴x+8=0 or x−3=0
⇒x=−8 or x=3 
Question 5 of 10
5. Question
The zeroes of a polynomial x^{2}−7x+12 are
Correct
x^{2}−7x+12
= x^{2}−4x−3x+12=0
= x(x−4)−3(x−4)=0
= (x−4)(x−3)=0
∴x−4=0 or x−3=0
⇒ x=4 or x=3Incorrect
x^{2}−7x+12
= x^{2}−4x−3x+12=0
= x(x−4)−3(x−4)=0
= (x−4)(x−3)=0
∴x−4=0 or x−3=0
⇒ x=4 or x=3 
Question 6 of 10
6. Question
A real number ‘k’ is said to be a zero of a polynomial p(x), if p(k) =
Correct
A real number ‘k’ is said to be a zero of a polynomial p(x), if p(k) is equals to 0.
if P(x) is a Polynomial in x and k is any real number,
then value of P(k) at x = k is denoted by P(k) is found by replacing x by k in P(x).
In the polynomial x^{2}–3x+2,
Replacing x by 1 gives,
P(1) = 1–3+2 = 0
Similarly, replacing x by 2 gives,
P(2) = 4–6+2 = 0
For a polynomial P(x), real number k is said to be zero of polynomial P(x), if P(k) = 0.Incorrect
A real number ‘k’ is said to be a zero of a polynomial p(x), if p(k) is equals to 0.
if P(x) is a Polynomial in x and k is any real number,
then value of P(k) at x = k is denoted by P(k) is found by replacing x by k in P(x).
In the polynomial x^{2}–3x+2,
Replacing x by 1 gives,
P(1) = 1–3+2 = 0
Similarly, replacing x by 2 gives,
P(2) = 4–6+2 = 0
For a polynomial P(x), real number k is said to be zero of polynomial P(x), if P(k) = 0. 
Question 7 of 10
7. Question
The zeroes of a polynomial x^{2}+4x+4 are
Correct
x^{2}+4x+4
= x^{2}+2x+2x+4
= x(x+2)+2(x+2)
= (x+2)(x+2)
∴x+2=0 or x+2=0
⇒x=−2 or x=−2Incorrect
x^{2}+4x+4
= x^{2}+2x+2x+4
= x(x+2)+2(x+2)
= (x+2)(x+2)
∴x+2=0 or x+2=0
⇒x=−2 or x=−2 
Question 8 of 10
8. Question
If the zeroes of a quadratic polynomial ax^{2} + bx + c, c ≠ 0 are equal, then
Correct
If the zeroes of a quadratic polynomial ax^{2}+bx+c,c≠0 are equal, then c and a have the same sign always.
Incorrect
If the zeroes of a quadratic polynomial ax^{2}+bx+c,c≠0 are equal, then c and a have the same sign always.

Question 9 of 10
9. Question
If a real number ‘α ’ is a zero of a polynomial, then ______ is a factor of f(x).
Correct
If a real number ′α′ is a zero of a polynomial then (x−α) is a factor of that polynomial.
Incorrect
If a real number ′α′ is a zero of a polynomial then (x−α) is a factor of that polynomial.

Question 10 of 10
10. Question
If ‘α’ and ‘β’ are the zeroes of a quadratic polynomial ax^{2}+bx+c, then α β =
Correct
If αα and β are the zeroes of a quadratic polynomial ax^{2}+bx+c,
∵ Product of the zeroes of a quadratic polynomial ax^{2}+bx+c = constant term/coefficient of x^{2}
thus, αβ=c/aIncorrect
If αα and β are the zeroes of a quadratic polynomial ax^{2}+bx+c,
∵ Product of the zeroes of a quadratic polynomial ax^{2}+bx+c = constant term/coefficient of x^{2}
thus, αβ=c/a