Multiple choice

Find all values of 'a', such that 4 lies somewhere between the roots of the equation 3x2 + 4ax + (a +3) = 0 for all values of x.

  1. a < −3

  2. a < −2

  3. a > 3

  4. a > 2
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A Correct answer
Explanation

For 4 to lie between the roots of the upward-opening quadratic, its value must make the quadratic negative. Substituting x = 4 gives 51 + 17a < 0, so a < -3.

AI explanation

For 4 to lie between the distinct roots of the quadratic equation 3x squared plus 4ax plus (a plus 3) equals 0, the value of the quadratic expression at x equals 4 must be strictly negative. Substituting x equals 4 gives 3 times 16 plus 4a times 4 plus a plus 3, which simplifies to 17a plus 51. Setting this less than zero gives 17a plus 51 is less than 0, so a is less than minus 3.

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