Multiple choice

To remove the second term of the equation $x^{4}-8x^{3}+x^{2}-x+3=0$, diminish the root of the equation by

  1. $1$
  2. $2$
  3. $3$
  4. $4$
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B Correct answer
Explanation

To remove the second term (x^3 term) of a polynomial, we shift the root by -a_n-1 / (n * a_n). Here, -(-8) / (4 * 1) = 8/4 = 2.

AI explanation

To remove the second term of a polynomial equation, we use the method of diminishing the roots, which requires shifting the variable by one-fourth of the coefficient of the second term. In the given equation x^4 - 8x^3 + x^2 - x + 3 = 0, the coefficient of the x^3 term is -8. Calculating one-fourth of this coefficient gives (-8)/4, which equals -2. To eliminate the term, we replace x with (y + 2), effectively diminishing the root of the equation by 2.

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