Multiple choice

Solve the given quadratic equations and answer the following question. Equation A: (x - 4)2 = (-5x)2 + 45 + 22x - R - 6 Equation B: (6t2 + 7t + 5 6 × ( 12 5 t − 18 ) ) = 0 One root of equation A is 8. Which of the following are the roots of equation B?

  1. − 5 2 and 3

  2. 1 and − 5 2

  3. -1 and 2 5

  4. 1 and − 2 5

  5. None of these
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B Correct answer
AI explanation

Substitute x = 8 into equation A to get (8 - 4)^2 = (-40)^2 + 45 + 22(8) - R - 6, which simplifies to 16 = 1600 + 45 + 176 - R - 6 and yields R = 1799. Since R does not affect the already provided equation B, we clear the parentheses in equation B to get 6t^2 + 7t + 2t - 15 = 0. Combining like terms gives the quadratic equation 6t^2 + 9t - 15 = 0, and dividing the entire equation by 3 yields 2t^2 + 3t - 5 = 0. Factoring this equation gives (2t + 5)(t - 1) = 0, so the roots are 1 and -5/2.

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