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NCERT Solutions for class 10 maths ex 2.4 Polynomials is discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. This class 10 ex 2.4 deals with polynomial and its types, algebraic expressions, degree of a polynomial expression, graphical representation of the polynomial equations, factorization, relationship between zeroes and coefficient of a polynomial.
Mathematically, the number of terms and the degree of the polynomial, polynomial can be classified into many types. Based on the number of terms, polynomials are classified as Monomial, Binomial and Trinomial. Also based on Degree, polynomials are classified as Linear Polynomial, Quadratic polynomial and Cubic Polynomial. Along with the Class 10 Maths chapter, 2 exercise 2.4 the following exercises are also present. Students should practice all problems discussed in these exercises to command the concepts.
Polynomials Class 10 Maths Chapter 2 Excercise: 2.4
Answer:
p(x) = 2x 3 + x 2 -5x + 2
p(1) = 2 x 1 3 + 1 2 - 5 x 1 + 2
p(1) =2 + 1 - 5 + 2
p(1) = 0
p(-2) = 2 x (-2) 3 + (-2) 2 - 5 x (-2) +2
p(-2) = -16 + 4 + 10 + 2
p(-2) = 0
Therefore the numbers given alongside the polynomial are its zeroes
Verification of relationship between the zeroes and the coefficients
Comparing the given polynomial with ax 3 + bx 2 + cx + d, we have
a = 2, b = 1, c = -5, d = 2
The roots are
Verified
Verified
Verified
Answer:
p(x) = x 3 - 4x 2 + 5x - 2
p(2) = 2 3 - 4 x 2 2 + 5 x 2 - 2
p(2) = 8 - 16 + 10 - 2
p(-2) = 0
p(1) = 1 3 - 4 x 1 2 + 5 x 1 - 2
p(1) = 1 - 4 + 5 - 2
p(1) = 0
Therefore the numbers given alongside the polynomial are its zeroes
Verification of relationship between the zeroes and the coefficients
Comparing the given polynomial with ax 3 + bx 2 + cx + d, we have
a = 1, b = -4, c = 5, d = -2
The roots are
Verified
Verified
Verified
Answer: Let the roots of the polynomial be
Hence the required cubic polynomial is x 3 - 2x 2 - 7x + 14 = 0
Q3 If the zeroes of the polynomial
Answer:
The roots of the above polynomial are a, a - b and a + b
Sum of the roots of the given plynomial = 3
a + (a - b) + (a + b) = 3
3a = 3
a = 1
The roots are therefore 1, 1 - b and 1 + b
Product of the roots of the given polynomial = -1
1 x (1 - b) x (1 + b) = - 1
1 - b 2 = -1
b 2 - 2 = 0
Therefore a = 1 and
Q4 If two zeroes of the polynomial
Answer: Given the two zeroes are
therefore the factors are
We have to find the remaining two factors. To find the remaining two factors we have to divide the polynomial with the product of the above factors
Now carrying out the polynomial division
Now we get
So the zeroes are
Answer: The polynomial division is carried out as follows
Given the remainder =x+a
The obtained remainder after division is
now equating the coefficient of x
which gives the value of
now equating the constants
Therefore k=5 and a=-5
Exercise 2.4 Class 10 Maths – consists of five problems in this section each containing a few sub-questions. In exercise 2.4 Class 10 Maths question 1 has two subsections where we need to check and demonstrate the relationship between the zeroes and the coefficients in each case. The remaining questions also support the zeros of a polynomial. And the last sum is based on the concept of division of a polynomial. The NCERT solutions for Class 10 Maths exercise 2.4 mainly focused on the zeroes of the polynomial, the relationship between the zeroes, the coefficients of the polynomial and the Division Algorithm. Two questions related to the division algorithm are given in exercise 2.4 Class 10 Maths.
Also see-
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
This ex 2.4 class 10 discussed concepts of terms, degrees and exponents in a polynomial. Practice the problems discussed in it to command the concepts. as per the above problem:
Terms : 6x^2, 5x, 18
Degree : 2
Exponents : 2 and 1
The class 10 maths ex 2.4 explains the concepts related to quadratic polynomial. A quadratic polynomial is nothing but a polynomial with degree two. The general form of a quadratic polynomial is ax^2 + bx + c = 0 where a, b, c are real numbers
The concepts related to quadratic polynomial are discussed in class 10 ex 2.4. Practice the problems discussed in this exercise to command these concepts. as per this problem the maximum index here is 2 . Also it is in the form of ax^2 + bx + c = 0.
Therefore 5x^2 + 6x + 54 = 0 is a quadratic polynomial.
n^2 - 10n + 24 = n^2 - 4n - 6n + 24
= n(n - 4) - 6(n - 4)
= (n - 4)(n - 6)
The number 9 can be written as 9x^0 which is a polynomial. Therefore 9 is a polynomial.
If p(x) and g(x) are any two polynomials where g(x) ≠ 0, p(x) = g(x) × q(x) + r(x).
That is Dividend = Divisor × Quotient + Remainder
NCERT solutions for Class 10 Maths chapter 2 exercise 2.4 consists of five problems and the questions are based on the concept of the division algorithm, to verify and prove the relationship between the zeroes, the coefficients and the zeros of a polynomial.
Hello
Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.
1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.
2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.
3. Counseling and Seat Allocation:
After the KCET exam, you will need to participate in online counseling.
You need to select your preferred colleges and courses.
Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.
4. Required Documents :
Domicile Certificate (proof that you are a resident of Karnataka).
Income Certificate (for minority category benefits).
Marksheets (11th and 12th from the Karnataka State Board).
KCET Admit Card and Scorecard.
This process will allow you to secure a seat based on your KCET performance and your category .
check link for more details
https://medicine.careers360.com/neet-college-predictor
Hope this helps you .
Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
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