Quadratic Polynomial

Q.

If $\alpha$ and $\beta$ are the zeroes of the polynomial $x^2-3x+k$, such that $\alpha -\beta =1$, find the value of $k$.

Q.

Verify whether the following are zeroes of the polynomial, indicated against them: $\mathrm{p}\left(\mathrm{x}\right)=3{\mathrm{x}}^2-1,\mathrm{x}=\frac{-1}{\sqrt{3}},\frac{2}{\sqrt{3}}$

Q. Find the area enclosed by the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Q. Find the area of the region in the first quadrant enclosed by $x-\text{axis}$, line $x=\sqrt{3}y$ and the circle $x^2+y^2=4$.

Q. Show that the complex number z, satisfying the condition $arg\left(\frac{z-1}{z+1}\right)=\frac{\pi }{4}$ lies on a circle.

Q.

A unit vector perpendicular to the plane formed by the points (1, 0, 1), (0, 2, 2) and (3, 3, 0) is:

1. 

2. 

3. 

4. 

Q. If $x^2-x+1=0$ then the value of ${(x+\frac{1}{x})}^2+{(x^2+\frac{1}{x^2})}^2+{(x^3+\frac{1}{x^3})}^2+{(x^5+\frac{1}{x^5})}^2$ is

Q. Consider a triangular surface whose vertex are three points having coordinates A(2a, 0, 0) B(0, a, 0)C(0, 0, a).If there is a uniform electric field (Ei+2Ej+3Ek) then flux linked to triangular surface ABC is

Q. Let $x,y\in Z$ such that $x^2-2x=y^2-2y+1010$. Then the number of pairs $(x,y)$ satisfying the equation is

1. only one
2. infinitely many
3. no such pair is possible
4. more than one but finite

Q.

The signs of the X, Y and Z coordinates of a point that lies in the octant OXYZ' is

1. ( + , - , -)

2. (- , + , +)

3. ( + , + , -)

4. (-, - , +)

Q.

Examine the following functions for continuity :

(d) $f\left(x\right)=|\times -5|$.

Q. Which of the following is/are a polynomial?

1. $3x^3+9x^{-1}+9$
2. $\sqrt{5}{x}^2+5x-7$
3. $8x^7-x^2+2\sqrt{3}$
4. $5\sqrt{x}+2x^2-4$

Q. Let $x,y\in Z$ such that $x^2-2x=y^2-2y+1010$. Then the number of pairs $(x,y)$ satisfying the equation is

1. only one
2. infinitely many
3. more than one but finite
4. no such pair is possible

Q. Ortho centre of the triangle whose vertices are (0, 0), (3, 0) and (4, 0) is .....................

1. (0, 0)

2. (3, 0)

3. (4, 0)

4. (3, 3)

Q. If the zeros of the quadratic polynomial $a{x}^2+bx+c,c\ne 0$ are equal, then

1. $c$ and $b$ have opposite signs
2. $c$ and $b$ have the same sign
3. $c$ and $a$ have opposite signs
4. $c$ and $a$ have the same sign

Q.

Differentiate $(x^2-5x+8)(x^3+7x+9)$in three ways mentioned below.

(a) By using product rule.

(b) By expanding the product to obtain a single polynomial.

(c) By logarithmic differentiation.

Do they all given the same answer?

Q. Prove that the curves $y^2=4x$ and $x^2=4y$ divide the area of the square bounded by $x=0,x=4,y=4$ and $y=0$ into three equal parts.

Q. The area between $x=y^2$ and $x=4$ is divided into two equal parts by the line $x=a$, find the value of $a$.

Q.

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 5y² – 9x² = 36

Q. Find the equation of parabola, of the focus is at (a, 0) and the vertex is at (a', 0)

Q. The zeroes of the polynomial $f\left(x\right)=x^2-3$ is

1. $3,-3$
2. $-\sqrt{3},\sqrt{3}$
3. $2,-2$
4. $0$

Q. If f(x)=x-1/x+1 then f(ax) in term of f (x) is given by

Q. F:R to R . F(x)=x^3+x-1. Find the solution of f(x)^-1

Q.

What does quadratic mean?

Q. Using integration find the area of the triangular region whose sides have the equations $y=2x+1,y=3x+1\text{and}x=4$.

Q.

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 49y² – 16x² = 784

Q. The degree of the polynomial $f\left(x\right)=(x^2-1)(x-3)$ is

Q. let f: R-R, f(x)= x^3 + x -1 find the solution of f(x)= f^-1 (x)

Q. If the graph of the quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$ is


Then, the possible value(s) of $a$ can be

1. $3$
2. $0$
3. $-2$
4. $-5$

Q.

find the value of $\underset{x\to \infty }{lim}\frac{2x^3-3x^2+5x+6}{7x^2+8x+15}$

1. 0

2. 6

3. 

4.