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7 February, 17:43

Which equation has the solutions x = (5 + - 2 / sqrt (7)) / (3) ?

A: 3x2 - 5x + 7 = 0

B: 3x2 - 5x - 1 = 0

C: 3x2 - 10x + 6 = 0

D: 3x2 - 10x - 1 = 0

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Answers (2)
  1. 7 February, 20:14
    0
    Recall the formula to find the solutions for an equation ax² + bx + c:

    x₁₂ = ( - b + / - √ (b²-4ac)) / 2a

    Since at the denominator of our solution we have 3, which is an odd number, therefore it cannot be 2a, but only a, we should use the formula:

    x₁₂ = (-β + / - √ (β²-ac)) / a

    Where β = b/2

    Hence, the only options that have an even number as b coefficient are C and D.

    Now, we need to find what values give √ (β² - ac) = 2√7 = √ (4·7) = √28:

    C) √ (β² - ac) = √ (25 - 3·6) = √7

    D) √ (β² - ac) = √ (25 - 3· (-1)) = √28

    Hence, the correct answer is D) 3x² - 10x - 1 = 0
  2. 7 February, 21:08
    0
    Which equation has the solutions?

    3x2 - 5x + 7 = 0 3x2 - 5x - 1 = 0 3x2 - 10x + 6 = 0 3x2 - 10x - 1 = 0
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