Polynomials Test

Result

Polynomials Test - 46

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Question 1
1 / -0

The roots of $$6x^{4}-35x^{3}+62^{2}-35x+6=0$$ are.......

A
2,-1/2,-1/3,3

B
2,1/2,3,1/3

C
-2,-1/2,-3,-1/3

D
2,1/2,-3,-1/3
Question 2
1 / -0

If $$p,\quad q,\quad r,\quad s\quad \in R$$, then equation $$({ x }^{ 2 }+{ px }+{ 3 }q)({ -x }^{ 2 }+rx+q)({ -x }^{ 2 }+sx-2q)=0$$ has

A
6 real roots

B
atleast two real roots

C
2 real and 4 imaginary roots

D
4 real and 2 imaginary roots

Solution
Question 3
1 / -0

If $$a,\beta ,y$$ are the roots of equation $${ x }^{ 3 }+2x-5=0$$ and if equation $${ x }^{ 3 }+{ bx }^{ 2 }+cx+d=0\quad has\quad roots\quad 2a+1.\quad 2\beta +1,\quad 2y+1.$$ then value of $$\left| b+c+d \right| $$ is (where b,c,dd are coprime ) -

A
41

B
39

C
40

D
43

Solution
Question 4
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
Sum of the roots of $$f ( x )$$ is equal to:

A
$$15$$

B
$$-15$$

C
$$21$$

D
Can't be determine

Solution
Question 5
1 / -0

Let for $$a \neq a_1 \neq 0, f(x) = ax^2 +bx +c, g(x) = a_1x^2 +b_1x+c_1$$ and $$p(x) =f(x) -g(x)$$. If $$p(x) =0$$ only for $$x- -1$$ and $$p(-2) =2$$ then the value of $$p(2)$$ is

A
$$18$$

B
$$3$$

C
$$9$$

D
$$6$$
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
Product of the roots of $$f ( x )$$ is equal to:

A
$$120$$

B
$$-120$$

C
$$114$$

D
$$-114$$

Solution
Question 7
1 / -0

The expansion $$\frac{1}{{\sqrt {4x + 1} }}\left[ {{{\left[ {\frac{{1 + \sqrt {4x + 1} }}{2}} \right]}^7} - {{\left[ {\frac{{1 - \sqrt {4x - 1} }}{2}} \right]}^7}} \right]$$ is a polynomial in x of degree

A
7

B
6

C
4

D
3

Solution
Question 8
1 / -0

The expression $${ \left[ x+{ \left( { x }^{ 3 }-1 \right) }^{ 1/2 } \right] }^{ 5 }+{ \left[ x-{ \left( { x }^{ 3 }-1 \right) }^{ 1/2 } \right] }^{ 5 }$$ is a polynomial of degree

A
5

B
6

C
7

D
8

Solution
Question 9
1 / -0

If a is a non-real root of $${ x }^{ 6 }=1$$, then $$\dfrac { { a }^{ 5 }{ a }^{ 3 }+a+1 }{ { a }^{ 2 }+1 } $$ is

A
$${ a }^{ 2 }$$

B
0

C
$${ -a }^{ 2 }$$

D
a

Solution
Question 10
1 / -0

The equation $${\left( {x - 3} \right)^9} + {\left( {x - {3^2}} \right)^9} + {\left( {x - {3^3}} \right)^9} + .... + {\left( {x - {3^9}} \right)^9} = 0\;has:$$

A
all the roots are real

B
One real and 8 imaginary roots

C
real roots namely $$x = 3,\;{3^2},{.....3^9}$$

D
Five real and 4 imaginary roots

Solution