Reduce the equation x⁴ − 13x² + 36 = 0 into a quadratic equation and find the roots of the reduced quadratic equation.

Correct option is A

Given:

​$$x^4 - 13x^2 + 36 = 0$$​​

Solution:

Let y = x², so the equation becomes:

$$y^2 - 13y + 36 = 0$$​​

​$$y^2 - 13y + 36 = 0$$​​

​$$y^2 - 9y - 4y + 36 = 0$$​​

(y - 9)(y - 4) = 0

y = 9  or y = 4

Roots of original equation are 9 and 4