Multiple choice

$kx^2-2\sqrt 5x +4 = 0$ For what value of $k$ will the quadratic equation have real and equal roots ?

  1. $\displaystyle \frac { 2 }{ 3 } $
  2. $\displaystyle \frac { 4 }{ 5 } $
  3. $\displaystyle \frac { 5 }{ 4 } $
  4. $\displaystyle \frac { 3 }{ 2 } $
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C Correct answer
Explanation

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

AI explanation

A quadratic equation has real and equal roots when its discriminant is zero. For the equation kx^2 - 2 times the square root of 5 multiplied by x + 4 = 0, we apply the discriminant formula of b^2 - 4ac to get (-2 times the square root of 5)^2 - 4(k)(4) = 0. Solving 20 - 16k = 0 yields k = 5/4.

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