Quadratic Polynomial

Q.

Find the zeros of the following quadratic polynomials $x^2+7x+10$ and verify the relationship between the zeros and the coefficients.

Q.

Equation of circle whose centre is origin and radius is 3 is:

1. x² + y² = 9

2. (x – h)² + (y – k)² = 9

3. x² + y² = 3

4. (x – h)² + (y – k)² = 3

Q. Number of the real solution of the equation |x-3|+2|x+1|=4

Q.

Without actual division prove that $X^4+2X^3+2X^2+2X-3$ is exactly divisible by $X^2+2X-3$.

Q.

Find the zeros of the following quadratic polynomials $x^2-1$ and verify the relationship between the zeros and the coefficients.

Q. If 2f(x)=f(xy)+f(x/y) for all positive values of x and y, f(1)=0 and f(1)=1, find the value of f(e).

Q. Solve for x, x^2-6x+[x]+7=0

Q.

The solution of the inequality 3(2-x) ≥ 2(1-x) for real x is:

1. x ≥ 4

2. x < 4

3. x > 4

4. x ≤4

Q.

The solution of the quadratic equation: x² -4x + 13 = 0

1. 2 ± 3i

2. 3 ± 2i

3. -2 ± 3i

4. -3 ± 2i

Q. if f(x+y) = f(x) * f(y) x, y belongs to R Find possible values of f(0) if f(0) is greater than 0

Q. A polynomial in which power of variable is 2, is called quadratic polynomial.

1. False
2. True

Q. Let $f\left(x\right)=x^5+a{x}^3+bx.$ The remainder when $f\left(x\right)$ is divided by $x+1$ is $-3.$ Then the remainder when $f\left(x\right)$ is divided by $x^2-1,$ is

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

Q. let f:R to R, f(x)=x³+x-1.find solution of f(x)=f^(-1)(x).

Q. In the triangle ABC with vertices A (2, 3), B (4, −1) and C (1, 2), find the equation and the length of the altitude from the vertex A.

Q. Equation of the hyperbola whose vertices are (± 3, 0) and foci at (± 5, 0), is
(a) 16x² − 9y² = 144
(b) 9x² − 16y² = 144
(c) 25x² − 9y² = 225
(d) 9x² − 25y² = 81

Q. The zeroes of the quadratic polynomial $f\left(x\right)=x^2+7x+10$ are

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

Q. Write the coordinates of the foci of the hyperbola 9x² − 16y² = 144.

Q. f(x+1)=x-1 find f(x)

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.

The complete set of values of k, for which the quadratic equation $x^2-kx+k+2=0$ has equal roots, consists of

1. 2 + √2

2. 2 ± √12

3. 2 - √12

4. -2 - √12

Q. The ends of the base of an isosceles triangle are at (2, 0) and (0, 1) and the equation of one side is x=2 then the orthocentre of triangle is

Q. 26. The function f(x)=0 has eight distinct solutions and f also satisfy f(4+x)= f(4-x). The sum of all eight solutions of f(x)=0 is

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

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

Q. find (1+x)6-(1-x)6 hence evaluate (1+root 3)6-(1-root 3)6

Q. find the value of x |x - 3| + |4 - x| = 1

Q. Write the solution of set of $\left|x+\frac{1}{x}\right|>2$.

Q. The number of points of integral coordinates that lie in the interior of the region common to the circle x^2 + y^2=16 and the parabola y^2=4x is?

Q. IF, f(x)=f(2-x) then f(-1)+f(3) = ?

Q. Find the coordinates of the orthocentre of the triangle whose vertices are (−1, 3), (2, −1) and (0, 0).