Quadratic Polynomial

Q. { Solve the equation }24x^3-14x^2-63x+λ=0 , one root being double of another. Hence tind the }}{ value(s) of }λ . }}{ Solve the equation }18x^3+81x^2+2x+60=0 , one root being half the sum of the other two. }}{ Hence find the value of }λ .

Q.

Q.

Which polynomial is a quintic binomial?

1. ${\mathrm{x}}^4-2{\mathrm{x}}^3-{\mathrm{x}}^2+7\mathrm{x}+11$

2. ${\mathrm{x}}^2+4\mathrm{x}$

3. $3{\mathrm{x}}^5+2$

4. $5{\mathrm{x}}^2-2\mathrm{x}+1$

Q. Question 19
For what valuel of m is $x^3–2m{x}^2+16$ is divisible by x +2?

Q. Question 21
If $a+b+c=0$, then $a^3+b^3+c^3$ is equal to

A) 0
B) 2ab
C) 3abc
D) 2abc

Q. A={x:xbelongs to Z, x is solution of x⁴-16=0}then A=

Q. Solve for x 9^x+6^x=2.4^x (1)0 (2)1 (3)+-2 (4)-1

Q. Find the remainder when $4x^3-3x^2+2x-4$ is divided by

(i) x - 1 (ii) x + 2 (iii) $x+\frac{1}{2}$

Q. If the discriminant of a quadratic equation is 0, then it has real and _______ roots.

1. distinct
2. imaginary
3. equal
4. unequal

Q. Identify constant, linear, quadratic and cubic polynomials from the following polynomials:

(iv) $p\left(x\right)=2x^2-x+4$

Q. The abscissa of a point A is equal to its ordinate, and its distance from the point B(1, 3) is 10 units, What are the coordinates of A?​

1. (-5, -5), (9, 9)
2. (0, 0), (9, -5)
3. (9, -5), (-5, 9)
4. (-9, -9), (5, 5)

Q. $-5$ is one of the zeroes of $2x^2+px-15$, zeroes of $p(x^2+x)+k$ are equal to each other. Find the value of $k$.

Q. If the discriminant of a quadratic equation is 0, then it has real and _______ roots.

1. equal
2. unequal
3. imaginary
4. distinct

Q. For what valuel of m is $x^3–2m{x}^2+16$ is divisible by x +2?

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 represented by the cubic polynomial $t\left(x\right)=p{x}^3+q{x}^2+rx+s$, then which of the following is always true?

1. $s\ne 0$
2. $r\ne 0$
3. $q\ne 0$
4. $p\ne 0$

Q. For what valuel of m is $x^3–2m{x}^2+16$ is divisible by x +2?

Q.

If $a+b+c=8$ and $ab+bc+ca=20$, find the value of $a^3+b^3+c^3–3abc$.

1. 48
2. 16
3. 64
4. 32

Q. The zeroes of the quadratic polynomial $a{x}^2+bx+c$ and the roots of the quadratic equation $a{x}^2+bx+c=0$ are equal.

1. True
2. False

Q. The discriminant of x^2 + 3x + 1 = 0 is

1. 10
2. 8
3. 6
4. 5

Q.

Quadratic equation is a polynomial of degree:

1. 4

2. 1

3. 2

4. 3

Q. The discriminant of 4x^2 + 4x + 1 = 0 is

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

Q. Zeros of the polynomial $x^2-4x-21$ are:

1. $3and7$
2. $-3and7$
3. $3and-7$
4. $-3and-7$

Q. If the discriminant of a quadratic equation is 0, then it has real and _______ roots.

1. equal
2. unequal
3. distinct
4. imaginary

Q. Q.4. If x + 1 / x = 2 find the value of $x^{99}+1/x^{100}$
Q.5. If x / y + y / x = - 1 (x, y $\ne$ 0), find the value of $x^3-y^3$.

Q. The graph of an equation is given above. What is the degree of the polynomial?

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

Q.

What are the minimum and maximum numbers of distinct real roots a quadratic equation can have?

1. 0, 1

2. 1, 1

3. 1, 2

4. 0, 2

Q.

What are the minimum and maximum numbers of distinct real roots a quadratic equation can have?

1. 0, 2

2. 0, 1

3. 1, 2

4. 1, 1

Q. Quadratic equations have only one root.

1. False
2. True

Q. Find the value of the polynomial $5x-4x^2+3$ at
(i) x = 0
(ii) x = - 1
(iii) x = 2 [3 marks]

Q. Solve this:
Q2. Find the value of the polynomial p(x) = 5x- 4x²+3 at x = -1
Q3. Write the coordinates of the origin? ​