Multiple choice

If the roots of the given equation $2x^2+3(\lambda -2)x+\lambda +4=0$ be equal in magnitude but opposite in sign, then value of $\lambda$ is

  1. $1$
  2. $2$
  3. $3$
  4. $\dfrac 23$
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B Correct answer
Explanation

If roots are equal in magnitude but opposite in sign, their sum must be 0. The sum of roots is -b/a = -3(lambda - 2)/2 = 0. Thus, lambda - 2 = 0, so lambda = 2.

AI explanation

For a quadratic equation where the roots are equal in magnitude but opposite in sign, the sum of the roots must equal zero. Using Vieta's formulas, the sum of the roots of 2x^2 + 3(lambda - 2)x + lambda + 4 = 0 is -3 times lambda minus 2 divided by 2. Setting this sum equal to zero gives the equation -3 times lambda minus 2 equals zero, so lambda minus 2 equals zero. Solving this gives the value of lambda as 2.

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