Question

alpha 10 & beta 10 Q. From the quadratic equation from the roots given below

Answer 1

 product of the roots = 0

⇒ x2 - Sx + P = 0, where S = sum of the roots and P = product of the roots ............... (i)

Formula (i) is used for the formation of a quadratic equation when its roots are given.

For example suppose we are to form the quadratic equation whose roots are 5 and (-2). By formula (i) we get the required equation as

x2 - [5 + (-2)]x + 5 ∙ (-2) = 0

⇒ x2 - (-3)x + (-10) = 0

⇒ x2 + 3x - 10 = 0


Solved examples to form the quadratic equation whose roots are given:

1. Form an equation whose roots are 2, and - 12.

Solution:

The given roots are 2 and -12.

Therefore, sum of the roots, S = 2 + (-12) = 32

And tghe product of the given roots, P = 2 ∙ -12= - 1.

Therefore, the required equation is x2 – Sx + p

i.e., x2 - (sum of the roots)x + product of the roots = 0

i.e., x2 - 32x – 1 = 0

i.e, 2x2 - 3x - 2 = 0


2. Find the quadratic equation with rational coefficients which has 13+2√2 as a root.

Solution:

According to the problem, coefficients of the required quadratic equation are rational and its one root is 13+2√2 = 13+2√2 ∙ 3−2√23−2√2 = 3−2√29−8= 3 - 2√2.

We know in a quadratic with rational coefficients irrational roots occur in conjugate pairs).

Since equation has rational coefficients, the other root is 3 + 2√2.

Now, the sum of the roots of the given equation S = (3 - 2√2) + (3 + 2√2) = 6

Product of the roots, P = (3 - 2√2)(3 + 2√2) = 32 - (2√2)2 = 9 - 8 = 1

Hence, the required equation is x2 - Sx + P = 0 i.e., x2 - 6x + 1 = 0.


2. Find the quadratic equation with real coefficients which has -2 + i as a root (i = √-1).

Solution:

According to the problem, coefficients of the required quadratic equation are real and its one root is -2 + i.

We know in a quadratic with real coefficients imaginary roots occur in conjugate pairs).

Since equation has rational coefficients, the other root is -2 - i

Now, the sum of the roots of the given equation S = (-2 + i) + (-2 - i) = -4

Product of the roots, P = (-2 + i)(-2 - i) = (-2)2 - i2 = 4 - (-1) = 4 + 1 = 5

Hence, the required equation is x2 - Sx + P = 0 i.e., x2 - 4x + 5 = 0.



 





11 and 12 Grade Math 

From Formation of the Quadratic Equation whose Roots are Given to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



HomeMath BlogMath Coloring PagesMultiplication TableCool Maths GamesMath Flash CardsOnline Math QuizMath PuzzlesPreschool ActivitiesKindergarten Math1st Grade Math2nd Grade Math3rd Grade Math4th Grade Math5th Grade Math6th Grade Math7th Grade Math8th Grade Math9th Grade Math10th Grade Math11 & 12 Grade MathAlgebra 1Concepts of SetsLogarithmsBoolean AlgebraStatisticsBinary SystemMath DictionaryConversion ChartHomework SheetsMath Problem AnsFree Math AnswersPrintable Math SheetFunny Math AnswersEmployment TestLink PartnersAbout UsContact UsSite Map

[?]Subscribe To This Site



E-mail AddressFirst NameThen

Don't worry — your e-mail address is totally secure.
I promise to use it only to send you Math Only Math.

 



Share this page: FacebookTwitter

© and ™ math-only-math.com. All Rights Reserved. 2010 - 2019.

This site uses cookies, some of which are required for its operation. Privacy policy.