SOLUTION: The equation {{{x^4 -6x^3 +7x^2 +6x-3=0}}} has irrational roots. Find them by expressing the equation in the form {{{(x^2 +ax)^2 +b(x^2 +ax) +c=0}}}.

Question 1126754: The equation has irrational roots. Find them by expressing the equation in the form .
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

We want to put the given 4th degree polynomial equation in the following form:

Expand this form and combine like terms:

We want this to be equal to

Solve for a, b, and c by equating coefficients.

x^4: the coefficients are both 1

x^3: --> a = -3

x^2: --> b = -2

x^1: (we already know that; if the product of our a and b were NOT 6, then the roots could not be found by this method)

x^0: c = -3

The equation in the new form is then

This is a quadratic equation with "x^2-3x" as the "variable". Factor and solve.

or

Neither of these quadratic expressions factors, so we get two pairs of irrational roots.

and
RELATED QUESTIONS
Write the equation in standard form y = ax^2 + bx + c if the roots are -4 and -2 and it... (answered by josgarithmetic,MathLover1)

find any rational roots for the equation: 6x^4 - 7x^3 + 8x^2 - 7x + 2 = 0 (answered by fractalier)

Use the quadratic formula to solve equation. Write irrational roots in the simplest... (answered by solver91311)

Solve for all (including irrational and complex roots if any) x in the equation... (answered by Edwin McCravy)

find all the roots of each equation.... (answered by glabow)

Find all the roots of the equation... (answered by stanbon)

Which of the following is the equation of the polynomial with roots at 0 and 3-√2... (answered by josgarithmetic)

find all the roots of each equation.... (answered by longjonsilver)

X^4+3X^3+9X^2+6X-12=0 find the roots of this... (answered by Edwin McCravy)