Multiple choice

For what real values of a do the roots of the equation $x ^ { 2 } - 2 x - \left( a ^ { 2 } - 1 \right) = 0$ Lie between the roots of the equation $x ^ { 2 }- 2 x ( a + 1 ) + a ( a - 1 ) = 0$

  1. $( - 1 / 4 < a < 1 )$
  2. $( 1 / 4 < a < 1 ) \text { and } ( a < - 1 / 3 )$
  3. $( - 1 / 2 < a < 1 ) \text { and } ( a < - 1 / 3 )$
  4. $( - 1 / 2 < a < 1 )$
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A Correct answer
Explanation

For the roots of one quadratic to lie between the roots of another, the function values at the roots of the second must have specific signs. Solving the conditions for the given equations leads to the interval -1/4 < a < 1.

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