Using substitution solving polynomial equations, Mathematics

Assignment Help:

Using Substitution Solving Polynomial Equations ?

Solve : (x3 + 4) 2 - 15 (x3 + 4) + 36 = 0.

You might be tempted to multiply everything out and factor. However, there's an easier way. Notice that this equation takes the form

A2 - 15A + 36 = 0,

where A = x3 + 4. You can easily solve this simpler quadratic equation! The left side factors to give

(A - 12)(A - 3) = 0

so A = 12 or A = 3.

Since A = x3 + 4, this is the same as saying

x3 + 4 = 12 or x3 + 4 = 3,

So x3 = 8 or x3 = -1,

which means

x = 2 or x = -1.

Normally, you can do this substitution of A for x3 + 4 in your head. You can simply write:

(x3 + 4) 2 - 15(x3 + 4) + 36 = 0

((x3 + 4) - 12)((x3 + 4) - 3) = 0

x3 + 4 = 12 or x3 + 4 = 3,

and so on.


Related Discussions:- Using substitution solving polynomial equations

Cylindrical coordinate system, how to describe the locus of the equation x^...

how to describe the locus of the equation x^2+6xy+y^2+z^2=1 in cylindrical polar coordinates?

Quadric surfaces - three dimensional spaces, Quadric Surfaces Earlier w...

Quadric Surfaces Earlier we have looked at lines and planes in three dimensions (or R 3 ) and when these are used fairly heavily at times in a Calculus class there are several

Simple harmonic motion, prove that the composition of two simple harmonic o...

prove that the composition of two simple harmonic of the same period and in the same straight line is also a simple harmonic motion of the same period.

Conic sections, The locus of the midpoint of the chords of an ellipse which...

The locus of the midpoint of the chords of an ellipse which are drawn through an end of minor axis is called

Using euclid''s algorithm find the value of x & y, If d is the HCF of 30, 7...

If d is the HCF of 30, 72, find the value of x & y satisfying d = 30x + 72y. (Ans:5, -2 (Not unique) Ans:    Using Euclid's algorithm, the HCF (30, 72) 72 = 30 × 2 + 12

Parametric equations of parabola., how the parametric equations of parabola...

how the parametric equations of parabola are derived?and what is the condition for the parabola whose equation is in the form of general equation of the two intersecting lines?

Math, weather prediction on monsoon past data on project

weather prediction on monsoon past data on project

Ratio and proportion, find the ratio of each of the following in simplest f...

find the ratio of each of the following in simplest form 1] 9 months to 7 by 4

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd