## NCERT Solutions Class 10 Maths Chapter-2 : Polynomials## Exercise 2.1
We can find the number of zeroes p(x) has by counting the points of intersection of the graph on X-axis. By applying this knowledge, we can conclude that the graphs have following numbers of zeroes: - No zeroes
- One zero
- Three zeroes
- Two zeroes
- Four zeroes
- Three zeroes
**x**^{2}- 2x - 8**4s**^{2}- 4s + 1**6x**^{2}- 3 - 7x**4u**^{2}+ 8u**t**^{2}- 15**3x**^{2}- x - 4
Hence, the given polynomial has two zeroes.
Hence, the given polynomial has two zeroes.
Hence, the given polynomial has two zeroes.
Hence, the given polynomial has two zeroes.
Hence, the given polynomial has two zeroes.
Hence, the given polynomial has two zeroes.
**1/4 , -1****√2, 1/3****0, √5****1, 1****-1/4, 1/4****4, 1**
## Exercise 2.3
**p(x) = x**^{3}- 3x^{2}+ 5x - 3, g(x) = x^{2}- 2**p(x) = x**^{4}- 3x^{2}+ 4x + 5, g(x) = x^{2}+ 1 - x**p(x) = x**^{4}- 5x + 6, g(x) = 2 - x^{2}
**t**^{2}- 3, 2t^{4}+ 3t^{3}- 2t^{2}- 9t - 12**x**^{2}+ 3x + 1, 3x^{4}+ 5x^{3}- 7x^{2}+ 2x + 2**x**^{3}- 3x + 1, x^{5}- 4x^{3}+ x^{2}+ 3x + 1
Since, the remainder is zero. Therefore, first polynomial is a factor of the second polynomial. Since, the remainder is zero. Therefore, first polynomial is a factor of the second polynomial. Since, the remainder is not zero. Therefore, first polynomial is not a factor of the second polynomial.
Putting the two zeroes in (x - a)(x - b) Now, 1/3 and 3x Therefore, 3x = (3x = (3x = (3x When (x + 1) = 0 � x = -1 and when (x + 1) = 0 � x = -1. Hence, the remaining two zeroes of the given polynomial are -1 and -1.
We know that, p(x) = g(x) × Quotient + Remainder Therefore, x x x On dividing x - 2 with x
**deg p(x) = deg q(x)****deg q(x) = deg r(x)****deg r(x) = 0**
I. p(x) = 8x q(x) = 4x g(x) = 2 r(x) = 0 II. p(x) = x q(x) = x - 3 g(x) = x r(x) = 7x - 9 III. p(x) = x q(x) = x - 1 g(x) = x r(x) = 5 ## Exercise 2.4 (Optional)
**2x**^{3}+ x^{2}- 5x + 2; 1/2 , 1, - 2**x**^{3}- 4x^{2}+ 5x - 2; 2, 1, 1
Now we will check if the given numbers are zeroes of the given polynomial by substituting them for x. Hence, the given numbers are the zeroes of the given polynomial.
Now we will check if the given numbers are zeroes of the given polynomial by substituting them for x. Hence, the given numbers are the zeroes of the given polynomial.
Solution Comparing the given polynomial with Ax A = 1, B = -3, C = 1, and D = 1
Substituting the two zeroes in (x - a) (x - b) Now, x Therefore, x = (x = (x = (x Hence, the two remaining zeroes will be 7 and -5.
First, we need to divide x Upon comparing the coefficients, we get two equations First equation - Second equation - Substitute k = 5 Hence, k = 5 and a = -5. Next TopicClass 10 Maths Chapter 3 |