Multiple choice

Solve the following quadratic equation by completing square. $2y^{2}\, +\, 5y\, +\, 1\, =\, 0$, then $y\, =\, \displaystyle \frac{-5\, \pm\, \sqrt{23}}{2}$. State true or false.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 2y^2 + 5y + 1 = 0, the quadratic formula is y = (-b +/- sqrt(b^2 - 4ac)) / 2a. Here a=2, b=5, c=1. y = (-5 +/- sqrt(25 - 8)) / 4 = (-5 +/- sqrt(17)) / 4. The statement provides sqrt(23) and denominator 2, which is incorrect.

AI explanation

To solve the quadratic equation 2y squared plus 5y plus 1 equals 0 by completing the square, we divide by 2 to get y squared plus (5 divided by 2)y plus (1 divided by 2) equals 0. Moving the constant gives y squared plus (5 divided by 2)y equals negative 1 divided by 2, and adding the square of half the coefficient of y, which is (5 divided by 4) squared or 25 divided by 16, yields (y plus 5 divided by 4) squared equals 25 divided by 16 minus 8 divided by 16, which is 17 divided by 16. Taking the square root of both sides and solving for y gives y equals (negative 5 plus or minus the square root of 17) divided by 4. Because this correct result differs from the stated expression, the given statement is false.

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