Question

Solve x4 - 9x² - 10=0 ​

Answer 1

Answer:

The roots of the equation are $\sf{\sqrt{-1}, \ -\sqrt{-1}, \ \sqrt{10}, \ and \ -\sqrt{10}}$

Given:

• The given equation is x⁴ - 9x² - 10 = 0

Solution:

=> x⁴ - 9x² - 10 = 0

=> (x²)² - 9x² - 10 = 0

Substitute x² = a

=> a² - 9a - 10 = 0

=> a² + a - 10a - 10 = 0

=> a (a + 1) - 10 (a + 1) = 0

=> (a + 1) (a - 10) = 0

=> a = - 1 or a = 10

When a = - 1

=> x² = - 1

On taking square root of both the sides

=> x = $\sf{\pm\sqrt{-1}}$ = $\sf{\pm \ i}$

When a = 10

=> x² = 10

On taking square root of both the sides

=> x = $\sf{\pm\sqrt{10}}$

Therefore, the roots of the equation are $\sf{\sqrt{-1}, \ -\sqrt{-1}, \ \sqrt{10}, \ and \ -\sqrt{10}}$