Question

x4 - 25x² + 144 = 0 solve quadritic equation​

Answer 1

Step-by-step explanation:

Given:-

x^4 - 25x^2 + 144 = 0

To find:-

Solve the equation ?

Solution:-

Given equation is x^4 - 25x^2 + 144 = 0

It can be written as is x^4 - 16x^2-9x^2 + 144 = 0

=>x^2(x^2-16)-9(x^2-16) = 0

=>(x^2-16)(x^2-9)=0

=>(x^2-4^2)(x^2-3^2)=0

We know that a^2-b^2 = (a+b)(a-b)

=>(x+4)(x-4)(x+3)(x-3) = 0

=>x+4 = 0 or x-4=0 or x+3 = 0 or x-3 = 0

=>x = -4 or 4 or -3 or 3

therefore,x = -4 , 4 , -3 ,3

Solution:-

The roots of the given equation are -4, -3, 3, 4

Additional information:-

• An equation of the degree 4 is called bi-quadratic equation.
• It has at most 4 roots.