Multiple choice

The values of k for which the roots are real and equal of the following equation $kx^2 - 2\sqrt{5}x + 4 = 0$ is $k =\dfrac{5}{4}$

  1. True

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

For real and equal roots, the discriminant D = b^2 - 4ac must be 0. D = (-2*sqrt(5))^2 - 4(k)(4) = 20 - 16k = 0. 16k = 20 => k = 20/16 = 5/4.

AI explanation

For the quadratic equation kx^2 - 2(root 5)x + 4 = 0 to have equal real roots, its discriminant (b^2 - 4ac) must equal zero. Substituting a = k, b = -2(root 5), and c = 4 gives (-2(root 5))^2 - 4(k)(4) = 0. This simplifies to 20 - 16k = 0, which means 16k = 20. Solving this yields k = 5/4, confirming the statement is True.

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