x^4-6x^3+9x^2=100 find the value of x
Answers
Step-by-step explanation:
x4+6x3+9x2=100
Four solutions were found :
x = 2
x = -5
x =(-3-√-31)/2=(-3-i√ 31 )/2= -1.5000-2.7839i
x =(-3+√-31)/2=(-3+i√ 31 )/2= -1.5000+2.7839i
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^4+6*x^3+9*x^2-(100)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(((x4)+(6•(x3)))+32x2)-100 = 0
Step 2 :
Equation at the end of step 2 :
(((x4) + (2•3x3)) + 32x2) - 100 = 0
Step 3 :
Checking for a perfect cube :
3.1 x4+6x3+9x2-100 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: x4+6x3+9x2-100
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 9x2-100
Group 2: 6x3+x4
Pull out from each group separately :
Group 1: (9x2-100) • (1)
Group 2: (x+6) • (x3)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = x4+6x3+9x2-100