Multiple choice

For what value of $k$ will the quadratic equation $\displaystyle { 2x }^{ 2 }+3x+k=0$ have real equal roots ?

  1. $\displaystyle \frac { 3 }{ 8 } $
  2. $\displaystyle \frac { 8 }{ 3 } $
  3. $\displaystyle \frac { 9 }{ 8 } $
  4. $\displaystyle \frac { 8 }{ 9 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0 to have real equal roots, the discriminant D = b^2 - 4ac must be zero. Here, 3^2 - 4(2)(k) = 0, so 9 - 8k = 0, which means k = 9/8.

AI explanation

To find when the quadratic equation has real equal roots, set the discriminant equal to zero. Using the formula D = b^2 - 4ac for 2x^2 + 3x + k = 0, we get (3)^2 - 4(2)(k) = 0. Solving 9 - 8k = 0 gives the value of k as 9/8.

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