Geometrical Representation of a Quadratic Polynomial

Q.

If one root of the equation 4x²− 2x + (λ−4) = 0 be the reciprocal of the other, then find the value of λ .

Is the answer: 8

Q. Graph of a quadratic polynomial is a

1. straight line
2. circle
3. parabola
4. ellipse

Q. Draw the graph of $y=x^2+3x+2$ and use it to sove the equation $x^2+2x+4=0$.

1. {1, 2}
2. {5, -6}
3. cannot be determined
4. No real roots

Q. Graph of a quadratic polynomial is a

1. straight line
2. circle
3. parabola
4. ellipse

Q.

The following graph corresponds to a

1. Quadratic polynomial

2. Bi- quadratic polynomial

3. Cubic polynomial

4. Linear polynomial

Q. If the solutions of the equation $x^2+3x-18=0$ are $-6,3$, then the roots of the equation $2(x^2+3x-18)=0$ are

1. -12, 6
2. -6, 3
3. -6, 6
4. 3, 3

Q.

Polynomials in Real Life

Polynomials are everywhere. It is found in a roller coaster of an amusement park, the slope of a hill, the curve of a bridge or the continuity of a mountain range. They play a key role in the study of algebra, in analysis and on the whole many mathematical problems involving them.

Based on the given information, answer the following question:

If the zeroes of the polynomial $p\left(t\right)=18t²+(3k-9)t+36$ are negative of each other, then find the value of $k$.

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

Q. The graph drawn below of a quadratic polynomial shows that it has no real roots.

1. True
2. False

Q. If the roots of the equation $x^2+3x-18=0$ are -6, 3 then the roots of the equation $2(x^2+3x-18)=0$ are

1. 3, 3
2. -6, 6
3. -12, 6
4. -6, 3

Q. Question 2 (iii)
Are the following statements ‘True’ or False’? Justify your answer.
iii) If the graph of a polynomial intersects the X-axis at exactly two points, it need not be a quadratic polynomial

Q. hree curves i.e.
a) $y=x^2$
b) $y=x^4$
c) $y=x^6$
are depicted in the graph shown below. Which of the polynomials does the graph 3 represent?

1. $y=x^2$
2. $y=x^4$
3. $y=x^6$
4. All of the above

Q. Three curves i.e. $a)y=x^2,b)y=4x^2\&c)y=8x^2$ are depicted in the following graph. Identify correct relation.

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

Q. The points at which the graph of a quadratic polynomial touch the $X$-axis are called the roots of the polynomial.

1. True
2. False

Q.

Which graph has a vertical stretch factor of $\frac{1}{2}$ whencompared to the graph of $y=x^2$?

1. 

2. 

3. 

4. 

Q.

Identify the linear graph among the following.

1. 1/(x-1)

2. √x + 2

3. √3 x + 5

4. None of these

Q. Three curves i.e.
a) $y=x^2$
b) $y=x^4$
c) $y=x^6$
are depicted in the graph shown below. Which of the polynomials does the graph 3 represent?

1. $y=x^2$
2. $y=x^4$
3. $y=x^6$
4. cannot be determined

Q. Choose the correct statements regarding the nature of curve formed by the graphical representation of the polynomial $a{x}^2+bx+c$ when $a=2,b=0,c=0$.

1. Curve is open upwards
2. Curve lies above and on the line $y=0$
3. Curve is symmetric about $x=0$
4. Curve is symmetric about y axis

Q. Three curves i.e. $a)y=3x^2,b)y=5x^2\&c)y=7x^2$ are depicted in the following graph. Identify correct relation.

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

Q. $Threecurvesi.e.a)y=3x^{2}b)y=5x^{2}c)y=7x^{2}Aredepictedinthefollowinggraph.Identifythecorrectrelation.$

1. (a)-(1) , (b)-(2), (c)-(3)

2. (a)-(2) , (b)-(3), (c)-(1)

3. (a)-(3) , (b)-(2), (c)-(1)

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

Q. The graph drawn below of a quadratic polynomial shows that it has two real and unequal roots.

1. True
2. False

Q. Which of the following is not the graph of a quadratic polynomial. Justify your answer

Q. What is the degree of the polynomial p(x)?

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

Q. The graph of a quadratic equation is a ______.

1. hyperbola
2. parabola
3. circle
4. ellipse

Q. Two curves i.e.
a) $y=-x^2$
b) $y=x^2$
are depicted in the following graph, Identify the correct relation.

1. (a)-(2) , (b)-(1)
2. None of the above
3. Both (A) & (B)
4. (a)-(1) , (b)-(2)

Q. If the solutions of the equation $x^2+3x-18=0$ are -6, 3, then the roots of the equation $2(x^2+3x-18)=0$ are _____.

1. -6, 6
2. -12, 6
3. -6, 3
4. 3, 3