Quadratic Polynomials

Q. If a quadratic polynomial f(x) is not factorizable into linear factors, then it has no real zero. (True/False)

Q.

Question 6
Is 0.2 a root of the equation $x^2$ – 0.4 = 0? Justify your answer.

Q. The polynomial which has the degree 2 is called as ______ polynomial.

1. Linear
2. Cubic
3. None of the above
4. Quadratic

Q. If a quadratic polynomial f(x) is factorizable into linear distinct factors, then what is the total number of real and distinct zeros of f(x)?

Q. What is the nature of the graph of quadratic polynomial?

1. Parabola
2. Hyperbola
3. Circle
4. Line

Q.

Find the quadratic equation whose roots are:

$2\sqrt{2}$ and $-3\sqrt{2}$

Q. If $a{x}^n+b{x}^{(n-1)}-1+c=0$ is a quadratic equation, then $n-1=$ ______.

1. 1
2. 2
3. 3
4. 4

Q.

Which of the following are not quadratic polynomials?
(i) $3+4x–7x^2$

(ii) $8x^2–15$

(iii) 6x – 15

(iv) $4x^3–3x$

(v) $x^2–x+1$

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.

If $\alpha$ and $\beta$ are the zeros of polynomial
$x^2+3x-2$, find $\frac{1}{(\alpha {)}^3}+\frac{1}{(\beta {)}^3}$.

1. $\frac{8}{45}$
2. $\frac{-8}{45}$
3. $\frac{45}{8}$
4. $\frac{45}{8}$

Q. Explain about quadratic polynomial.

Q.

A quadratic equation consists of a polynomial of degree ___ .

Q.

What is the graph of $-x^2+5x-6$?

1. 

2. 

3. 

4. 

Q. Which of the following is not a graph of a quadratic polynomial?

(a)
(b)
(c)
(d)

Q. What is the degree of a quadratic polynomial?

1. 1
2. 3
3. 2
4. 0

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.

Find a quadratic polynomial for the bridge if 6 is the sum and 8 is the product of its zeroes.

1. $x^2+6x+8$
2. $x^2-6x+8$
   
3. $x^2+6x-8$
4. $x^2-6x-8$

Q. Which of the following is not a quadratic equation?
[1 mark]

(a) $2(x-1{)}^2=4x^2-2x+1$
(b) $2x-x^2=x^2+5$
(c) ${(\sqrt{2}x+\sqrt{3})}^2=3x^2-5x$
(d) $(x^2+2x{)}^2=x^4+3+4x^3$

Q. Question 6
Is 0.2 a root of the equation $x^2$ – 0.4 = 0? Justify your answer.

Q.

Classify the following as a constant, linear, quadratic, and cubic polynomials:

$1+x+x^2$

Q. If $a{x}^n+b{x}^{(n-1)}-1+c=0$ is a quadratic equation, then n =

1. 1
2. 2
3. 3

Q. Check whether the following is a quadratic equation:
$(x-2)(x+1)=(x-1)(x+3)$
(2 Marks)

Q.

Give an example of a linear, quadratic and qubic polynomial that doesnt have its zero of the polynomial!

Q.

Quadratic equation consists a polynomial of degree:

1. 4

2. 1

3. 2

4. 3

Q. If the graph of a quadratic polynomial is a downward opening parabola, then its quadratic coefficient is a .

1. positive number
2. negative number
3. natural nunber
4. whole number

Q. The simplified form of the expression given below is :$\frac{\frac{y^4-x^4}{x(x+y)}-\frac{y^3}{x}}{y^2-xy+x^2}$

1. $1$
2. $2$
3. $-1$
4. $0$

Q. Which among the following is a quadratic polynomial?

1. $x^2+5x-14$
2. $x^3-4x^2$
3. $3x-4$
4. $3x^4-4x$

Q. If $a{x}^n+b{x}^{(n-1)}-1+c=0$ is a quadratic equation, then $n-1=$ ______.

1. 1
2. 2
3. 3
4. 4

Q. If $a{x}^n+b{x}^{(n-1)}-1+c=0$ is a quadratic equation, then n =

1. 1
2. 2
3. 3
4. 4

Q.

Quadratic equation is a polynomial of degree ____________

1. 1

2. 2

3. 4

4. 3

Q. The quadratic coefficient of the polynomial ($5x^2+6x+9$) is 5.

1. True
2. False

Q. The coefficient of $x$ in the quadratic equation $a{x}^2+bx+c=0$ is called the linear coefficient.

1. True
2. False