Question

The roots of the equation x⁴-2x³+x=380 are:

• A. \(5,-4,\dfrac{1\pm5\sqrt{-3}}{2}\)
• B. \(-5,4,\dfrac{1\pm5\sqrt{-3}}{2}\)
• C. \(5,4,\dfrac{-1\pm5\sqrt{-3}}{2}\)
• D. -5,-4,dfrac1±5√(-3)2

Hint:

Try integer roots first using the Remainder Theorem.

Answer 1

The Correct Option is A

Step 1: Check integral roots: x=5,-4 satisfy the equation.
Step 2: Factoring out gives remaining quadratic: x²-x+19=0
Step 3: Solving, x=frac1±5√(-3)2