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Exercise 1. So, it can be written in the form of 2m. Case I : n is even, i. Hence, we can conclude from above two cases that if n is odd, then n 2 � 1 is divisible by 8. Question 5 The largest number which divides 70 and , leaving remainders 5 and 8, respectively, is A 13 B 65 C D Solution: A Since 5 and 8 are the remainders of 70 and , respectively. Question 8 The product of a non-zero rational and an irrational number is A always irrational B always rational C rational or irrational D one Solution: A Product of a non-zero rational and an irrational number is always irrational.
Justify your answer. Solution: No. Is this statement true or false? Give reasons. So, one integer out of these two must be divisible by 2. Hence, product of two consecutive integers is divisible by 2. So, one integer of these three must be divisible by 2 and another one must be divisible by 3. Hence, product of three consecutive integers is divisible by 6.
Question 6 The numbers and are both divisible only by 3, 5, 15, 25 and What is HCF , ? The highest common factor among these is Hence, it is a composite number. Give reasons for your answer. Solution: After simplification denominator has factor 5 3. So, this is terminating decimal. Question 10 A rational number in its decimal expansion is Solution: So, it represents a rational number and also its denominator must have the form 2 m x 5 n.
Thus, Question 11 Which of the following is not the graph of a quadratic polynomial? These curves are called parabolas. So, option D cannot be possible.
Also, the curve of a quadratic polynomial crosses the X-axis at most two point but in option D , the curve crosses the X-axis at the three points, so it does not represent the quadratic polynomial. So, division algorithm is not satisfied. So the given statement is not correct. Justify your answers. As, a polynomial of degree more than 2 is possible which intersects the x-axis at exactly two points when it has two real roots and other imaginary roots.
Then, product of zeroes Given that, all three zeroes are positive. So, the product of all three zeroes is also positive. Thus, their sum is also positive. Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:.
Question 1 For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
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