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

1 Answer | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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.

We’ve answered 318,988 questions. We can answer yours, too.

Ask a question