Multiple choice

The roots of the quadratic equation 5x2 - 14x - 3 = 0 are

  1. 1/5, 3

  2. 5, 1/3
    • 1/5, 3

  4. 1/5, - 3
    • 1/5, - 3
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C Correct answer
Explanation

Using the quadratic formula x = (-b +/- sqrt(b^2 - 4ac)) / 2a, for 5x^2 - 14x - 3 = 0, we get x = (14 +/- sqrt(196 - 4*5*(-3))) / 10 = (14 +/- sqrt(256)) / 10 = (14 +/- 16) / 10. The roots are 30/10 = 3 and -2/10 = -1/5.

AI explanation

To solve 5x^2 - 14x - 3 = 0, we use the quadratic formula with the coefficients a = 5, b = -14, and c = -3. The discriminant calculates as b^2 - 4ac = (-14)^2 - 4(5)(-3) = 196 + 60 = 256. Taking the square root of the discriminant gives 16, so the roots are x = (14 + 16) / 10 = 3 and x = (14 - 16) / 10 = -1/5.

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