Cubic Polynomial

Q.

What is a quadratic polynomial?

Q.
The above picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.

Based on the above information, answer the following questions.

Find a quadratic polynomial with $\frac{1}{8}$ as the sum and 2 as product of its zeroes.

1. $8x^2+x+16$
2. $8x^2-x+16$
3. $8x^2-x-16$
4. $8x^2+x-16$

Q.

Is Root $3$ a polynomial?

Q.

Classify the following as linear, quadratic and cubic polynomials: $3t$

Q. Write the standard form of a cubic polynomial with real coefficients.

Q. If alpha beta and gamma areroots of cubic polynomial of p (x) is equal to 4x cube plus 3 x square minus 5 x square minus 7 then 1 upon alpha plus 1 upon beeta plus 1 upon alpha is equal to

Q.

Classify the following as linear, quadratic and cubic polynomials: $7x^3$

Q.

If ${(x}^4+x^{2}y+y^2)$ is one of the factors of an expression which is the difference of two cubes, then the other factor is ___.

1. $x^2-y$
2. $x-y^2$
3. $x-y$
4. $x^2-y^2$

Q.

Classify the following as linear, quadratic and cubic polynomials.

(1)$x^2+x$

(2)$x-x^3$

(3)$y+y^2+4$

(4)1 + x

1. Quadratic, cubic, quadratic, linear

2. Quadratic, quadratic, quadratic, linear

3. Cubic, cubic, quadratic, quadratic

4. Linear, cubic, quadratic, linear

Q. Verify that the numbers given along side of the cubic polynomials below are their zeros. Also, verify the relationship between the zeros and coefficients in each case:

(i) $f\left(x\right)=2x^3+x^2-5x+2;\frac{1}{2},1,-2$
(ii) g(x) = x³ − 4x² + 5x − 2; 2, 1, 1

Q. Given that the zeroes of the cubic polynomial $f\left(x\right)=x^3-6x^2+3x+10$ are of the form $a,a+b,a+2b$ for some real numbers $a$ and $b$, find the values of $a$ and $b$ as well as the zeros of the given polynomial.

Q. Considering the graph of the polynomial $x^n$, what can be the possible value of 'n'?

1. 6
2. 5
3. 4
4. 2

Q. 82 is a polynomial of degree .

1. \N
2. 1
3. 2
4. 82

Q. How many zeros does cubic polynomial has?

Q.

Polynomials are everywhere. It is found in the slope of a hill, the curve of a bridge or the continuity of a mountain range.

Based on the given information, answer the following question.

If the hills are prepresented by the cubic polynomial $t\left(x\right)=2x^3+8x^2+9x+16,$ then the product of the zeroes is:

1. $-4$
2. $\frac{9}{2}$
3. $-8$
4. $8$

Q. If the zeros of the polynomial f(x) = x³ − 3x² + x + 1 are (a − b), a and (a + b), Find a and b.

Q.

Classify the following as linear, quadratic and cubic polynomials: $r^2$

Q.

Write the coefficient of $x^2$ in each of the following?
(1) $2+x^2+x$
(2) $2-x^2+x^3$
(3) $\frac{\pi }{2}{x}^2+x$
(4) $\sqrt{2}x-1$

1. $1,-1,\frac{\pi }{2},\sqrt{2}$

2. $1,1,1,\sqrt{2}$

3. $1,-1,\sqrt{2},\pi$

4. $1,-1,\frac{\pi }{2},0$

Q. Match the following columns
$\begin{array}{cc}P\left(x\right)& \text{Type of Polynomial}\\ a)40x-323& 1)\text{Quadratic Polynomial}\\ b)x^3+456x^2-6x+11& 2)\text{Linear Polynomial}\\ c)91x^2-5x+\sqrt{2}& 3)\text{Cubic Polynomial}\end{array}$

1. a-2, b- 1, c -3
2. a-3, b- 2, c -1
3. a-1, b- 3, c -2
4. a-2, b- 3, c -1

Q. If one of the zeroes of the cubic polynomial ax^3+bx^2+d is zero. Then find product of other two zeroes

Q.

What is the coefficient of $z$ in $(z-5{)}^3$?

1. 125

2. -25

3. 5

4. 75

Q. If one of the zeros of the cubic polynomial ax³ + bx2 + cx + d is 0, then the product of the other two zeros is

(a) $\frac{-c}{a}$
(b) $\frac{c}{a}$
(c) 0
(d) $\frac{-b}{a}$

Q. Which of the following is a cubic polynomial ?

1. $x^2+4x-7$
2. $3x^2+4$
3. $x^3+3x^2-4x+3$
4. $3(x^2+x+1)$

Q. Match the following columns
$\begin{array}{cc}P\left(x\right)& \text{Type of Polynomial}\\ a)40x-323& 1)\text{Quadratic Polynomial}\\ b)x^3+456x^2-6x+11& 2)\text{Linear Polynomial}\\ c)91x^2-5x+\sqrt{2}& 3)\text{Cubic Polynomial}\end{array}$

1. a-3, b- 2, c -1
2. a-2, b- 1, c -3
3. a-2, b- 3, c -1
4. a-1, b- 3, c -2

Q. Which of the following is NOT a cubic polynomial?

1. $p\left(x\right)=\frac{x^3}{3}$
2. $p\left(x\right)=x^3-x^2$
3. $p\left(x\right)=\frac{0x}{x}+3x^3$
4. $p\left(x\right)=(x-1)(x+1)$

Q. Which of the following is a cubic monomial?

1. $4x^3+2x+6$
2. $x+5$
3. $9x^3$
4. $2x^2+2x+7$

Q. Classify the following as a constant, linear quadratic and cubic polynomials:
$2-x^2+x^3$

Q. Which of the following are not a cubic polynomial?

1. $p\left(x\right)=x^3-3x^2+10$
2. $p\left(x\right)=\frac{1}{3}{x}^2-6x+14$
3. $p\left(x\right)=x^3-24x$
4. $p\left(x\right)=x^2-2x+6$

Q. Classify whether $x-x^3$ is linear, quadratic, or a cubic polynomial.

Q.

Find the condition that the zeros of the polynomial $f\left(x\right)=x^3+3p{x}^2+3qx+r$ may be in A.P.