Which of these equations would not be in quadratic form?
A.X^4-13X^2+36=0
B.2X^(2/5)+X^(1/5)-6=0
C.6x^3+2x^2-8X=0
D.3(2/x-4)^2+5(2/x-4)-2=0
I think its between C or D. C because the exponents are different not doubled and D because its set up is completely the opposite from all the others.
It is in fact C
D is just a quadratic in (2/x-4), because if you substitute u=2/x-4, you have just 3u^2+5u-2=0
It is C because as you say, there is not
a term with twice the exponent of the other.
76
To determine which equation is not in quadratic form, we need to understand what quadratic form means. A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants. So, we are looking for the equation that does not have this specific format.
Let's analyze each given equation:
A. X^4 - 13X^2 + 36 = 0: This equation is in quartic form, not quadratic form. The highest exponent is 4, which makes it a quartic equation.
B. 2X^(2/5) + X^(1/5) - 6 = 0: This equation is expressed with fractional exponents, but it can be rewritten in quadratic form by substituting a variable. Let's say Y = X^(1/5). So the equation becomes 2Y^2 + Y - 6 = 0, which is in quadratic form.
C. 6x^3 + 2x^2 - 8X = 0: This equation is a cubic equation, not quadratic. It contains an x^3 term, which is the highest exponent.
D. 3(2/x-4)^2 + 5(2/x-4) - 2 = 0: This equation may look different from the others, but it is indeed in quadratic form, although it is expressed with fractions and variable substitutions. By substituting Y = 2/(x-4), we can rewrite the equation as 3Y^2 + 5Y - 2 = 0, which is now in quadratic form.
Therefore, the equation that is not in quadratic form is option C. 6x^3 + 2x^2 - 8X = 0. It is a cubic equation. Option D. 3(2/x-4)^2 + 5(2/x-4) - 2 = 0 is in quadratic form, despite its unique structure.