Solving Polynomial Equations, in Depth
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Problems 9
- Given that 8x3+12x2+6x=2158x^3+12x^2+6x=2158x3+12x2+6x=215 for a real number xxx, find the value of xxx. Express your answer as a fraction pq\frac{p}{q}qp in lowest terms, with…
- How many distinct positive real roots does the equation log10(x6)=(log10x)3\log_{10}(x^6) = (\log_{10}x)^3log10(x6)=(log10x)3 have?
- Find the value of xxx such that 6xy−4y+3x−2=06xy - 4y + 3x - 2 = 06xy−4y+3x−2=0 is true for all values of yyy.
- How many real roots does x3+x2=−x−1x^3+x^2 = -x-1x3+x2=−x−1 have?
- How many real solutions does (x+1)3+(x−1)3=0(x+1)^3 + (x-1)^3 = 0(x+1)3+(x−1)3=0 have?
- Jared wants to make a box. The possible heights xxx of the box satisfy the equation x3−4x2−x+4=0x^3-4x^2-x+4 = 0x3−4x2−x+4=0. Select the heights that the box can be.
- I'm thinking of a real number. The cube of this number minus two times the square of the number plus four times this number equals eight. What is this number?
- Which of the following is not equivalent to 2x3−4x2+8x=02x^3 - 4x^2 + 8x = 02x3−4x2+8x=0?
- Which of the following is not equivalent to the following equation: x4+4x3−12x2=0x^4+4x^3-12x^2=0x4+4x3−12x2=0