Solve with quadratic equation

Question

Solve a^4-10a^2+9=0

Answer 1

a⁴ - 10a² + 9 = 0

 

Note that we expect 4 roots because the power

of this polynomial is 4

 

The basic format for the quadratic equation is

ax² + bx + c

 

We want the powers of the variable to be

2 and 1 .... The way to approach this is to

choose a variable to represent a² ...

If we let x=a² and replace that in your

equation it becomes:

 

x² - 10x + 9 = 0

This is a quadratic which can be solved.

 

x = [-b ±√(b²-4ac)]/2a    a=1, b=-10, c=9

 

x = [10 ±√((-10)²-4(1)(9))]/2(1)

 

= [10 ±√(100-36)]/2

 

= (10 ±√64)/2

 

= (10 ± 8)/2

 

x = 18/2   or   2/2

 

x = 9 or 1

 

Remember that x = a²  so..

 

a² = 9   or   a² = 1

a = ±√9 = ±3   or  a = ±√1 = ±1

 

a = 3, -3, 1, -1

 

Hope this helps.  Let me know if you have questions.