Multiple choice

If roots of equation ${6x}^{2}-7x+k=0$ are equal. find $k$.

  1. $\dfrac{49}{24}$
  2. $-2$
  3. $-1,-2$
  4. $1,2$
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A Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac must be 0. Here a=6, b=-7, c=k. So (-7)^2 - 4(6)(k) = 0, which means 49 - 24k = 0, so k = 49/24.

AI explanation

For a quadratic equation to have equal roots, its discriminant must be equal to zero according to the properties of quadratic equations. For the equation 6x^2 - 7x + k = 0, the discriminant is b^2 - 4ac, which translates to (-7)^2 - 4 multiplied by 6 multiplied by k. Setting this equal to zero gives 49 - 24k = 0. Solving for k yields k = 49/24.

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