Polynomials Test

Result

Polynomials Test - 45

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Weekly Quiz Competition

Question 1
1 / -0

The zeros of the polynomial $${ x }^{ 2 }-9$$ are

A
3,3

B
$$\sqrt { 3 } ,-\sqrt { 3 } $$

C
3,-3

D
$$-\sqrt { 3 } ,-\sqrt { 3 } $$

Solution
Question 2
1 / -0

For equation $${ x }^{ 3 }-{ 6x }^{ 2 }+9x+k=0$$ to have exactly one root in (1, 3), the set of values of k is

A
(-4, 0)

B
(1, 3)

C
(0, 4)

D
None of these

Solution
Question 3
1 / -0

If the sum of two roots of the equation $${ x }^{ 3 }-p{ x }^{ 2 }+qx-r=0$$is zero, then

A
pq=r

B
qr=p

C
pr=q

D
pqr=1

Solution
Question 4
1 / -0

Number of root of equation
3|x|-|2-x|=1
is

A
0

B
2

C
4

D
7
Question 5
1 / -0

The roots of the equation $$\left( x-1 \right) ^{ 3 }+8=0$$ are

A
$$-1,1+2\omega ,1+{ 2\omega }^{ 2 }$$

B
$$-1,1-2\omega ,1-{ 2\omega }^{ 2 }$$

C
$$2,2\omega ,{ 2\omega }^{ 2 }$$

D
$$2,1+2\omega ,1+{ 2\omega }^{ 2 }$$

Solution
Question 6
1 / -0

Let $$f ( x )$$ be a polynomial of degree 5 with leading coefficient unity, such that $$f ( 1 ) = 5 , f ( 2 ) = 4 , f ( 3 ) = 3 , f ( 4 ) = 2$$ and $$f ( 5 ) = 1 ,$$ then
$$f ( 6 )$$ is equal to:

A
$$120$$

B
$$-120$$

C
$$0$$

D
$$6$$

Solution
Question 7
1 / -0

Number of common roots of the equation $$x^4+x^2+1=0$$ and $$x^8-1=0$$ is

A
zero

B
1

C
2

D
4

Solution
Question 8
1 / -0

The product of the zero of the polynomal $${ x }^{ 2 }-4x+3$$ is ....

A
4

B
1

C
-4

D
3

Solution
Question 9
1 / -0

If the sum of two roots of the equation $$\displaystyle x^3 px^2 + qx r = 0$$ is zero , then

A
pq = r

B
qr = p

C
pr = q

D
pqr = 1

Solution
Question 10
1 / -0

If $$f(x)={ 4x }^{ 4 }-{ ax }^{ 3 }+{ bx }^{ 2 }-cx+5$$ (a, b, c $$\in $$ R) has four positive real zeros $${ r }_{ 1 },{ r }_{ 2 },{ r }_{ 3 },{ r }_{ 4 }$$ such that $$\frac { { r }_{ 1 } }{ 2 } +\frac { { r }_{ 2 } }{ 4 } +\frac { { r }_{ 3 } }{ 5 } +\frac { { r }_{ 4 } }{ 8 } =1$$, then a is equal to

A
19

B
20

C
21

D
22

Solution