Multiple choice

Find the real roots of the quadratic equation x2 – 9x + 18 = 0 and for the two roots x and x1, find a and b such that Log10 a = x and Log10 b = x1.

  1. 18, 6

  2. 103, 109

  3. 106, 103

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Factoring x^2 - 9x + 18 gives (x - 3)(x - 6) = 0, so the roots are 3 and 6. Since log10 a = x and log10 b = x1, the corresponding values are powers of 10, namely 10^3 and 10^6. Option C lists these values in reverse order, which is allowed because the roots can be labeled either way.

AI explanation

To find the roots, factor the quadratic equation x^2 - 9x + 18 = 0 into (x - 3)(x - 6) = 0. This gives the two real roots as x = 3 and x1 = 6. Using the given logarithmic conditions, Log10 a = 3 and Log10 b = 6. Converting these from logarithmic to exponential form gives a = 10^3 and b = 10^6. Therefore, the values of a and b are 10^3 and 10^6, respectively.

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