# 2X^4+(H-2)X^3-5X^2+X+(K-3)=0 Find h and k if equation is: 1 reciprocal 2 biquadratic

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Expert Answers

sciencesolve | Certified Educator

1) You need to remember what is the form of reciprocal equation if the polynomial is of fourth order:

`ax^4 + bx^3 + cx^2 + bx + a = 0`

Notice that the free term needs to be equal to the coefficient of `x^4` , hence `k - 3` needs to be equal to 2 such that:

`k-3 = 2 =gt k = 2+3 =gt k = 5`

Notice that the coefficient of `x^3` needs to be equal to the coefficient of x, hence `h - 2` needs to be equal to 1 such that:

`h - 2 = 1 =gt h = 3`

**Hence, for `k = 5 ` and `h = 3` , the reciprocal equation is `2x^4 + x^3 - 5x^2 + x + 2 = 0.` **

2) **You need to remember that a biquadratic equation does no have odd powers, hence the given equation can not be a biquadratic, because it contains the term x.**