Multiple choice

Value of k for which the roots are real and equal of the following equation $2kx^2$ - 40x + 25 = 0 is $k = 8$

  1. True

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

For the quadratic equation 2kx^2 - 40x + 25 = 0 to have real and equal roots, the discriminant D = b^2 - 4ac must be 0. Here, (-40)^2 - 4(2k)(25) = 1600 - 200k = 0, which gives k = 8.

AI explanation

The condition for the equation 2kx^2 - 40x + 25 = 0 to have real and equal roots is that its discriminant (b^2 - 4ac) is zero. Here a = 2k, b = -40, and c = 25, so setting the discriminant to zero gives (-40)^2 - 4(2k)(25) = 0. This expands to 1600 - 200k = 0, meaning 200k = 1600. Solving for k gives k = 8, which makes the statement True.

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