Question

what substitution should be used to rewrite 4x^12 - 5x^6 - 14 =0 as a quadratic equation? a. u=x^2 b. u=x^3 c. u=x^6 d. u=x^12

Answer 1

u=x^6...................................

Answer 2

The substitution that can be made in order to convert the equation into quadratic equation is:

`u=x^6`

Hence, option: C is correct.

Explanation:

We are asked to find the substitution that can be made in order to convert the given degree six polynomial equation into a quadratic equation i.e. degree 2.

We are given a polynomial equation as:

`4x^(12)-5x^2-14=0`

We know that a quadratic equation is written in the form:

`ax^2+bx+c=0`

where a,b and c are real numbers.

Hence here if we substitute:

`u=x^6`

We get:

`u^2=x^(12)`

Hence, the equation get converted into:

`4u^2-5u-14=0`

Hence, the substitution is:

`u=x^6`