Polynomials Test

Result

Polynomials Test - 47

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Weekly Quiz Competition

Question 1
1 / -0

The roots of the equation $$ax^3 + bx^2 - x + 1=0$$ are real, distinct and are in H.P., then

A
$$b$$ $$\epsilon$$ $$(-\infty,\frac{1}{3})$$

B
$$a$$ $$\epsilon$$ $$(-\frac{1}{27},\infty)$$

C
$$27a + 9b=2$$

D
None of these

Solution
Question 2
1 / -0

The expression $$(x+(x^4-1)^{1/2})^4 + (x-(x^4-1)^{1/2})^4$$ is a polynomial of degree

A
8

B
6

C
4

D
2

Solution
Question 3
1 / -0

The sum of the roots of the equation $$cot-1x-1(x+2)=150$$ is

A
0

B
1

C
2

D
-2

Solution
Question 4
1 / -0

If $$\alpha ,\beta ,\gamma $$ are roots of $$7{ x }^{ 3 }-x-2=0$$ then find the value of $$\sum { \left( \dfrac { \alpha }{ \beta } +\dfrac { \beta }{ \alpha } \right) } $$

A
1

B
2

C
-3

D
-4

Solution
Question 5
1 / -0

If roots of equation $$8x^3 -14x^2+7x-1 =0$$ are in geometric progression, then roots are

A
$$3,6,8$$

B
$$1,2,4$$

C
$$2,4,8$$

D
$$1,1/2,1/4$$

Solution
Question 6
1 / -0

If $$1,-2,3$$ are the roots of $${ x }^{ 3 }-b{ x }^{ 2 }+ax+6=0$$, then a=

A
$$-5$$

B
$$5$$

C
$$2$$

D
none of these

Solution
Question 7
1 / -0

number of real roots of the equation
$$\sqrt { x } +\sqrt { x-\sqrt { 1-x } } =1\quad is$$

A
0

B
1

C
2

D
3

Solution
Question 8
1 / -0

The HCF of two ploynomials $$A$$ and $$B$$ using long division method was found to be $$2x + 1$$ after two steps . The fisrt two quotient obtained are $$x$$ and $$(x + 1)$$ . Find $$A$$ and $$B$$ . Given that degree of $$A$$ > degree of $$B$$ is

A
$$A = 2x^3 + 3x^2 + x - 1 $$ ; $$B = 2x^2 - 3x + 1 $$

B
$$A = 2x^3 - 3x^2 + x - 1 $$ ; $$B = 2x^2 - 3x - 1 $$

C
$$A = 2x^3 + 3x^2 - 3x - 1 $$ ; $$B = 2x^2 - 3x + 1 $$

D
$$A = 2x^3 + 3x^2 + 3x + 1 $$ ; $$B = 2x^2 + 3x + 1 $$

Solution
Question 9
1 / -0

The root of the equation $${ X }^{ 4 }-1=0$$ are;

A
1,1,i,-i

B
1,-1,i,-i

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

D
none of these

Solution
Question 10
1 / -0

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

A
7

B
5

C
4

D
3

Solution