Multiple choice

Which of the following can be that possible equation whose roots are 10 times the roots of the given equation? 2x2 – 15x + 18 = 0

  1. x2 + 75x + 900 = 0

  2. x2 - 75x - 900 = 0

  3. x2 + 75x - 900 = 0

  4. x2 - 75x + 900 = 0

  5. Both (3) and (4)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If roots are 10 times the original roots, replace x with x/10 in the original equation: 2(x/10)^2 - 15(x/10) + 18 = 0. 2(x^2/100) - 1.5x + 18 = 0. Multiply by 50: x^2 - 75x + 900 = 0.

AI explanation

To find an equation whose roots are 10 times the roots of 2x^2 - 15x + 18 = 0, substitute x/10 for x in the original polynomial. This gives the new equation 2(x/10)^2 - 15(x/10) + 18 = 0, which simplifies to x^2/50 - 3x/2 + 18 = 0. Multiplying the entire equation by 50 to clear the denominators results in x^2 - 75x + 900 = 0.

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