Polynomial

Q. The sum of two natural numbers is 8 and their product is 15. Find the numbers. [CBSE 2012]

Q.

Half the Perimeter of a rectangular garden whose length is4 meter more than its width is36 meter. Find the dimensions of the garden

Q. On dividing $3x^3+x^2+2x+5$ by a polynomial g(x), the quotient and remainder are (3x-5) and (9x+10) respectively. Find g(x).

Q. Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?

Q. Split the middle term for x²-x-2

Q.

Find the four numbers in AP whose sum is 50 and in which the greatest number is 4 times the least .

Q.

if the given polynomial $x^2-2x-\sqrt{5}$. Find value of $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$

Q. Which of the following is/are not polynomial(s)?

1. $3$
2. $4x^2+5\sqrt{x}$
3. $\sqrt{3}{x}^3+x+1$
4. $4x+5$

Q. Some students planned a picnic. The budget for food was Rs. 480. But eight of these failed to go and thus the cost of food for each member increased by Rs. 10. How many students attended the picnic?

Q. If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.

Q.

The highest exponent of a variable in a polynomial is called degree of the polynomial. Is this statement true or false?

1. True

2. False

Q. Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.

Q. Show that p(x)=x^3 - 3x^2 + 2x - 6 has only one real zero.

Q. Define a polynomial with real coefficients.

Q.

The graph of the polynomial p(x) intersects the x-axis three times in distinct points, then which of the following could be an expression for p(x):

1. x² - 9

2. 3x + 3

3. 3x² + 3x - 3

4. 4 - 4x - x² + x³

Q. FUNCTIONS If f(x) is a polynomial satisfying f(x).f(y) = f(x) + f(y) + f(xy) - 2, for all x, y belong to R and f(2) = 5, then show that f(x) is an even function.

Q.

Solve the following quadratic equation by factorization method

1/a+b+x = 1/a + 1/b +1/x , a and b is not equal to zero

Q. $\mathrm{If}A\mathrm{is}\mathrm{square}\mathrm{matrix}\mathrm{of}\mathrm{order}n,\mathrm{then}\left|\mathrm{adj}\right(A\left)\right|=$

1. $|A{|}^{n-1}$
2. $|A{|}^n$
3. $|A{|}^{n-2}$
4. $\left(A\right|$

Q.

Some students planned a picnic. The total budget for hiring a bus was Rs.1440. Later on, eight of these refused to go and instead paid their total share of money towards the fee of one economically weak student, and thus the cost of each member, who went for picnic increased by $Rs.30$
How many students attended the picnic and how much money was paid towards the fees?

Q. for polynomial x2-2x-root 5, find (alpha2-beta2)-(alpha-beta)2+(alpha+beta)2

Q.

A trader brought a number of articles for Rs. 900, five articles were found damaged. He sold each of the remaining articles at Rs.2 more than what he paid for it. He got a profit of Rs.80 on the whole transactions. Find the number of articles he bought.

Q. A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. one less, the cost would remain unchanged. How long is the piece?

Q.

The maximum number of zeroes the polynomial $x^7$+ $x^5$ + $x^3$ + x + 1 can have is

1. 0

2. 5

3. 7

4. 6

Q.

An expression in which the variables involved have only whole numbers as exponents is called a polynomial .then what are those expressions whose power is not a whole number ?

Q.

Let a, b, c, p be rational numbers such that p is not a prrfper cube, if a+bp^1/3+cp^2/3=0. Then prove that a=b=c=0.

Q.

The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Their present ages are

1. 6 and 14

2. The situation is not possible

3. 2 and 18

4. 10 and 10

Q.

Which of the following is not a polynomial ?

(a) $\sqrt{3}{x}^2-2\sqrt{3}x+5$ (b) $9x^2-4x+\sqrt{2}$

(c) $\frac{3}{2}{x}^3+6x^2-\frac{1}{\sqrt{2}}x-8$ (d) $x+\frac{3}{x}$

Q.

The value of the polynomial: -5x + 3 at x=0 is

1. -2

2. 3

3. 0

4. 8

Q.

The value of quadratic polynomial f (x)=2x²- 3x- 2 at x =-2 is ……

1. 15

2. 16

3. -12

4. 12

Q. ntIf the value of a quadratic polynomial p(x) is 0 at x = -1 and p(-2) =2 , then the value of p(2) isn ntA) 18n ntB) 9n ntC) 6n ntD) 3n