UrbanPro
true

Take Class 10 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Polynomials {Class-10 / CBSE}

Optimize Tutorials
21/04/2018 0 0

Polynomial - Concept

A polynomial is a mathematical expression consisting of the sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient.

 Zeroes of a Polynomial.

  • Mathematically: K is said to be zero of a polynomial p(x) if p(k) = 0
  • Graphically: Values of x coordinates where Polynomial P(x) crosses/touches the x-axis are called zeros of polynomial P(x).

Some Graphs:

  •     Graph of a linear polynomial ax + b is a straight line.
  •     Graph of a quadratic polynomial p(x) = ax2+ bx + c is a parabola open upwards like ∪, if a > 0.
  •     Graph of a quadratic polynomial p(x) = ax2+ bx + c is a parabola open downwards like ∩, if a > 0.
  •     In general, a polynomial p(x) of degree n crosses the x-axis at at-most n points.


The relationship between zeroes and the coefficients of a Quadratic Polynomial :

  •     If α, β are zeroes P(x) = ax2 + bx + c, then


                           

  •     If α, β are roots of a quadratic polynomial p(x), then.

P(x) =K {x2 – (sum of roots) x + product of roots}

P(x) = K {x2 + (α+ β) x +(αβ)}

 
The relationship between the zeroes and the coefficients of a Cubic Polynomial

If α, β and γ are zeroes of a cubic polynomial p(x),

P(x) = K {x3 – (sum of zeroes) x2 + (sum of product of zeroes) x – (product of zeroes)}

P(x) = K {x3 – (α + β + γ) x2 + (αβ + βγ + αγ) x – (αβγ)}

0 Dislike
Follow 3

Please Enter a comment

Submit

Other Lessons for You

Rotation of a Shape
* Rotation is nothing but rotating an object through an angle of 90 degrees, 180 degrees, 270 degrees either clockwise or anticlockwise. * For rotating 90 degrees clockwise and anticlockwise the steps...

Dhaturoop with meaning
विधिलिड्. लकार: (possibility and prayer ) पुरुष: एकवचनम् अर्थ द्विवचनम् अर्थ बहुवचनम् अर्थ प्रथमपुरुष: पठेत् पढ़ना चाहिए पठेताम् (दो को )...

Polynomials Class 10 Basics of Chapter 2
A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, combined using the operations of addition, subtraction, and multiplication. The variables...

Verb formation (लोट् लकार = Request or Order )
लोट् लकार (अनुज्ञा, Imperative Mood) पुरुष एकवचन द्विवचन बहुवचन प्रथमपुरुष तु ...

SURFACE AREA OF CUBE
#As shown in the above diagram The cube has 6 square surfaces.they are equal in area. # The cube has 12 equal edges or sides TOTAL SURFACE AREA OF CUBE:- If edge(side) of the cube = a Then,Total...
X

Looking for Class 10 Tuition Classes?

The best tutors for Class 10 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 10 Tuition with the Best Tutors

The best Tutors for Class 10 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more