Polynomials Formulas Class 10
Polynomials formulas class 10 enable students to understand the relationship between the zeroes and the coefficients of polynomials along with their geometrical representations. Thus, having a clear understanding of these formulas is highly crucial for students to solve various problems. To help students learn and memorize the polynomials formulas class 10 with ease this article provides a list of all important formulas, solved examples and memorization tips.
List of Polynomials Formulas Class 10
Students can refer to the list of polynomials formulas class 10 provided below.
- Polynomials consisting of 1, 2 and 3 degrees are known as linear, quadratic and cubic polynomials.
- Quadratic Polynomial: A quadratic polynomial is of the form ax2 + bx + c, with real coefficients, where a, b, c are real numbers with a not equal to zero.
- Roots of a Quadratic Polynomial: A quadratic polynomial can have maximum 2 zeros while a cubic polynomial can have 3.
- Sum of Roots of a Quadratic Polynomial:α +β = -b/a, where α and β are the zeroes of the quadratic polynomial ax2 + bx + c.
- Product of roots of a quadratic polynomial: αβ=c/a. where α and β are the zeroes of the quadratic polynomial ax2 + bx + c.
- Sum of Roots of a Cubic Polynomial: If the zeroes of the cubic polynomial ax3 + bx2 + cx + d, are α, β, γ then, sum of its roots is: α + β + γ = -b/a And product of its roots is: αβ+ βγ + γα = c/a, αβ γ = -d/a
Applications of Polynomials Formulas Class 10
Polynomials are helpful in expressing many real-world problems thus these formulas are widely applied in various fields and occupations. Some of the useful applications of polynomial formulas class 10 are listed below:
- Polynomials formulas class 10 are widely used in the business world to determine factors like wages, overhead costs, payroll, taxes, etc.
- Among professions, economists utilize these polynomials formulas to evaluate economic growth patterns and other values.
- Polynomials formulas are widely used in higher calculations by engineers designing various machinery.
- These formulas are also used in the medical field by medical researchers to describe the behavior of bacterial colonies.
Tips to Memorize Polynomials Formulas Class 10
Students can follow the below-mentioned tips to memorize polynomials formulas class 10:
- Learn polynomial formulas logically with some interactive resources as it will make learning more engaging.
- In addition to practicing problems based on formulas, try to read the theory and examples provided in the textbook for a deeper understanding of concepts.
- Students should discuss and clear their doubts with their teachers or friends to have clarity on them. It will help in getting a good hold of these formulas and their applications.
- Students can easily download the polynomial formulas sheet from the internet and apply them as wallpaper on their smartphones and laptops to revise. This will allow them to perform revision anytime.
Polynomials Formulas Class 10 Examples
Example 1: Create a quadratic equation whose roots are 3 and 5. Also, find the relation between the coefficients of the quadratic equation and its roots.
Solution: For x = 3 and x = 5 the value of the quadratic equation is equal to zero.
Thus, (x - 3) ( x-5) = 0
Expanding the equation, x2 - 5x - 3x + 15 = 0
==> x2 - 8x + 15 = 0
We can see that, sum of zeroes is 8 = - ( coefficient of x) / coefficient of x2
Also, the product of zeroes is 15 = coefficient of constant / coefficient of x2
The students can download the printable Maths Formulas Class 10 sheet from below.
FAQs on Polynomials Formulas Class 10
What are Important Concepts related to Polynomials Formulas Class 10?
Some of the important concepts related to polynomials formulas class 10 are listed below:
- Polynomials consisting of 1, 2 and 3 degrees are known as linear, quadratic and cubic polynomials.
- A quadratic polynomial is of the form ax2 + bx + c, with real coefficients, where a, b, c are real numbers with a not equal to zero.
- A quadratic polynomial can have maximum 2 zeros while a cubic polynomial can have 3.
- If the zeroes of the quadratic polynomial ax2 + bx + c, are α and β, α + β = - b/a and αβ = c/a.
- If the zeroes of the cubic polynomial ax3 + bx2 + cx + d, are α, β, γ then, α + β + γ = -b/a, αβ + β γ + γ α = c/a, αβ γ = - d/a
Why is it Important to Practice Problems Based on Polynomials Formulas Class 10?
Practicing problems based on polynomials formulas class 10 will help students understand linear and quadratic polynomials, their zeros, the relation of zeroes of a quadratic function to its coefficients and the division algorithm which states that any polynomial p(x) can be expressed in the form g(x) * r(x) + t(x).
How Many Formulas are there in polynomials formulas class 10?
There are three main formulas in Polynomials formula chapter 10.
- For any quadratic polynomial ax2 + bx + c having α and β as the roots, then
α + β = −b/a and αβ = c/a.
- For any quadratic polynomial ax3 + bx2 + cx + d having α , β and γ as the roots, then
α + β + γ = - b/a and αβ+ β γ + γ α = c/a and αβ γ = -d/a
- The division algorithm states that given any polynomial p(x) and any non-zero
polynomial g(x), there are polynomials q(x) and r(x) such that
p(x) = g(x) q(x) + r(x),
where r(x) = 0 or degree r(x) < degree g(x).
How can I Memorize Polynomial Formulas Class 10?
Students can refer to some below-mentioned tips that will help them memorize the polynomial formulas class 10 more effectively:
- Try to understand the logical explanation of each formula. It will enable you to memorize it better while solving problems.
- Clarify all your doubts and read terms carefully before memorizing polynomials formulas class 10. It will help you in better understanding all concepts.
- Use formula images as smartphones and laptops to revise them.
Where to find Polynomial Formulas Class 10?
Students can find the printable polynomial formulas class 10 sheet provided on this page. They can follow a few simple steps to download it. By downloading these formulas students will be able to understand and revise all important polynomial formulas.