Polynomial

Q.

What is the degree of the zero polynomial?

Q.

If 2 to the power a = 3 to the power b = 6 to the power c, find the relation between a, b, c .

Q.

The length of a rectangle is twice its breadth .if it's length is decreased by 5 cm and the breadth is increased by 5cm, the area of the rectangle is increased by 75 cm2.the length of the rectangle is:

Q.

What is the degree of a non-zero constant polynomial?

Q. An entity whose value varies or changes or is not constant is called _______ .

1. variable
2. constant
3. expression
4. degree

Q. The exponent of a variable in a polynomial must be a rational number.

Q. Find the zero of polynomial 3x+ 6

Q. The zero of the polynomial ($x-5$) occurs at $x$ =

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

Q.

If √a + √b + √c = 0, then the value of (a + b - c) whole square = ?

Q. (i) Give an example of a binomial of degree 27.
(ii) Give an example of a monomial of degree 16.
(iii) Give an example of a trinomial of degree 3.

Q. Is x = 2 a zero of the polynomial $x^2-4?$

Q. Question 1
Which of the following expressions are polynomials? Justify your answer.
I. $8$
II. $\sqrt{3}{x}^2-2x$
III. $1-\sqrt{5x}$
IV. $\frac{1}{5x^{-2}}+5x+7$
V. $\frac{(x-2)(x-4)}{x}$
VI. $\frac{1}{x+1}$
VII. $\frac{1}{7}{a}^3-\frac{2}{\sqrt{3}}{a}^2+4a-7$
VIII. $\frac{1}{2x}$

Q. 17.A AND B HAVE SOME MARBLES N IF A GIVES SOME MARBLES TO B, THEN B WILL HAVE TWICE AS MANY MARBLES AS A. IF B GIVES SOME MARBLES TO A, THEN A WILL HAVE THRICE AS MANY MARBLES AS B. WHAT IS THE MINIMUM POSSIBLE VALUE OF N FOR WHICH THE ABOVE STATEMENTS ARE TRUE?

Q. If x represents a whole number, then which of the following expressions can represent any positive odd integer?

1. 2x +1
2. x+1
3. 3x + 4
4. 2x

Q.

When five pens were bought together, the total price was reduced by three rupees and only seventeen rupees had to be paid. Had they been bought one by one, how much would have been the price of each pen?

Q. If f(X)=0 is a polynomial and f(a), f(b) have opposite sign, then f(X)=0 has atleast one real root in the interval (a, b) Prove the statement

Q. I have some tables and chairs. If I place two chairs at each table, I have one extra chair. If I place three chairs at each table, I have one table with no chairs. What is the sum of the total number of tables and chairs?

Q.

Question 1
Which one of the following is a polynomial?

A) $\frac{x^2}{2}-\frac{2}{x^2}$
B) $\sqrt{2x}-1$
C) $x^2+\frac{3x^{\frac{3}{2}}}{\sqrt{x}}$
D) $\frac{x-1}{x+1}$

Q. if the polynomial 16x^4-24x^3+41x^2-mx+16 be a perfect square, then the value of m is

Q. Find the quotient when $x^3-2x^2-11x+12$ is divided by $x-1$

1. $x^2-x+12$
2. $x^2+x+12$
3. $x^2-x-12$
4. $x^2+x-12$

Q.

Expressions that contain only two terms are known as:

1. Binomials

2. Monomials

3. Trinomials

4. Equations

Q. If $x=\frac{1}{2}$ is a zero of the polynomial $f\left(x\right)=8x^3+a{x}^2–4x+2,$
find the value of a.

Q.

There are 'a' trees in the village Lat. If the number of tree increase every year by 'b' , then how many trees will be there be after 'x' year

Q. 18. Verify that the numbers given alongside alongside of the polynomial are their zeroes. also verify the relationship between the zeros and the coefficient.x*4+2x*3-7X*2-8x+12; -3, -2, 1, 2

Q. For polynomial p(x) = –3x2 + 7x – 2, the sum of maximum value of polynomial and the point where polynomial p(x) attains maximum value, is

Q. Find the roots of the following quadratic equations by the factorisation method: 21x^2 – 2x + 121 = 0

Q.

Write the coefficient of $a$ in the following.

$4a$

Q. Zero of the polynomial p(x) = 2x - 10 is _____.

1. 10
2. 5
3. -5
4. 0

Q. P_1^{}(x) = ax^2-bx-c, P_2^{}(x) = bx^2-cx-a, P_3(x) = cx^2-ax-b be three quadritic polynomials . Suppose there exists a real number α such that P_1 (α) = P_2(α) = P_3(α). Prove that a =b= c

Q. Verify whether the following are true or false.
(i) -3 is a zero of x - 3
(ii) $-\frac{1}{3}$ is a zero of 3x + 1
(iii) $-\frac{4}{5}$ is a zero of 4 - 5y
(iv) 0 and 2 are the zeroes of $t^2–t$