Multiple choice

If one root of quadratic equation ${ \left( K+1 \right) }^{ }{ x }^{ 2 }-5x+2K=0$ is reciprocal of other, then the value of $K$ is :

  1. $2$
  2. $0$
  3. $-1$
  4. $1$
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D Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0, if roots are reciprocals, then c/a = 1. Here, 2K / (K+1) = 1 => 2K = K + 1 => K = 1.

AI explanation

If the roots are reciprocals of each other, their product must equal 1. Using the product of roots formula, the product of the roots is 2K / (K + 1). Setting this equal to 1 gives 2K / (K + 1) = 1. Solving this equation yields 2K = K + 1, which means K = 1. The result is 1.

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