Polynomials-linear equation test paper

10TH Mathematics
Section A
Solve any five of the following 5x3=15
1. Find the value of a and b for which the following system of linear equations has infinite numbers of solutions:
2x - 3y = 7 (a + b) x - (a + b - 3)y = 4a + b.) Solve the following system of linear equations

2. For what value of k will the system of equations

x + 2y = 5; 3x + ky + 15 = 0 has (i) unique solution (ii) no solution

3. solve the following system of linear equations: ax + by = c, b x + ay = 1 + c 4

4. Find a quadratic polynomial whose the sum and product of its zeros respectively. √3,2

5. If a and b are the zeros of a given quadratic polynomial f(x) = x2 + x - 2, find the value of 1/a + 1/b

6. If 2, ½ are the zeros of px2+5x+r, prove that p= r.

Section B       Solve any five questions 5x4=20

1. Find the zeros of the quadratic polynomial x2+ 9x + 20 , and verify the basic relationships between the zeros and the coefficients.

2. Five years ago, Neeta was trice as old as Reeta. Ten years later, Neeta will be twice as old as Reeta, How old are Neeta and Reeta now?

3. Person can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find man’s speed of rowing is still water and the speed of the current.

4. The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.

5. There are two class rooms A and B containing students. If 5 students are shifted from room A to room B, the resulting number of students in the two rooms become equal. If 5 student are shifted from room B to room A, the resulting number of student's in room A becomes double the number of student left in room B. find the original number of student in the two rooms separately.

6. Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time . If they moves in the same direction, they meet in 8 hours and if they move in opposite directions, they meet in 1 hours and 20 minutes. Find the speed of the cars.

7. If a & ß are the zeroes of the polynomial 2x2 _ 4x + 5, then find the value of a3 + ß3

Polynomial test paper for class 10

CBSE TEST PAPER O1 

   10th Polynomial         

1. Write the zeroes of the polynomial x² -2x + 4.

2. Find a quadratic polynomial, the sum and product of whose zeroes are 0 and √5  respectively.

3. Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively

4. If a andb are the zeros of the quadratic polynomial f(x)= x²-5x+4, find the value of 1/a  + 1/b-2a b

5. Find the zeroes of the quadratic polynomial 4 √3 x² + 5 x - 2 √3 and verify the relationship between the zeroes and the coefficients.

6. Find the zeroes of the quadratic polynomial 4u² + 8u and verify the relationship between the zeroes and the coefficients

7. Find the quadratic polynomial, the sum and product of whose zeroes are √2 and √3 respectively.

8. If a and b are the zeros of the given quadratic polynomial f(x)= 5x² - 7x + 1, find the value  1/a  + 1/b

9. Find the zeroes of the polynomial x² – 3 and verify the relationship between the zeroes and theCoefficients

10. Find the remainder when p(x)= x³-6x²+2x-4 when divided by  1 - 2x.

11. Find the remainder when x⁵¹+51 is divided by (x+1).

12. Find all the integral zeros of x³ -3x² - 2x + 6

13. Obtain all zeros of 3x⁴ + 6x³ - 2x² - 10x - 5, if two of its zeros are √5/√3 and - √5/√3

14. If (x - 2) and [x – ½ ] are the factors of the polynomials qx² + 5x + r prove that q = r

15. If the zeroes of the polynomial are 3x² − 5x + 2 are a+ b and a- b, find a and  b.

16. On dividing 2x2 + 3x + 1 by a polynomial g(x), the quotient and the remainder were 2x-1 and 3 respectively. Find g (x).

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What is a rational number?

What is a rational number?

 

Any ordinary number of arithmetic:  Any whole number, fraction, mixed number or decimal; together with its negative image.

A rational number is a nameable number, in the sense that we can name it according to the standard way of naming whole numbers, fractions, and mixed numbers.  "Five," "Six thousand eight hundred nine," "Nine hundred twelve millionths," "Three and one-quarter," and so on.

Q. Which of the following numbers are rational?

1

−6

3½

−

2 3

0

5.8

3.1415926535897932384626433

A rational number can always be written 

a b	, where a and b are integers (b  0).

An integer itself can be written as a fraction:  b = 1.  And fromarithmetic, we know that we can write a decimal as a fraction.

When a and b are positive, that is, when they are natural numbers, then we can always name their ratio.  Hence the term, rational number.

At this point, the student might wonder, What is a number that is not rational?

An example of such a number is  ("Square root of 2").  It is not possible to name any whole number, any fraction or any decimal whose

square is 2.

7 5

is close, because

7 5

·

7 5

=

49 25

-- which is almost 2.