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

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

Hence, option: C is correct.

Step-by-step 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:

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

where a,b and c are real numbers.

Hence here if we substitute:

We get:

Hence, the equation get converted into:

Hence, the substitution is:

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.