Multiple choice

If the roots of the equation (4 - a)x2 + 2(a + 2)x + 8a + 1 = 0 are equal, then the values of a are

  1. 3, 1

  2. 4, - 2

  3. 0, 3

  4. 2, - 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac must be zero. Here, [2(a+2)]^2 - 4(4-a)(8a+1) = 0. Expanding this gives 4(a^2 + 4a + 4) - 4(32a + 4 - 8a^2 - a) = 0, which simplifies to 9a^2 - 27a = 0. Solving 9a(a-3) = 0 gives a = 0 or a = 3.

AI explanation

For the roots to be equal, the discriminant b^2 - 4ac must equal zero. Substituting a = 4 - a, b = 2(a + 2) and c = 8a + 1 gives the equation [2(a + 2)]^2 - 4(4 - a)(8a + 1) = 0. Expanding and simplifying this expression results in 3a^2 - 9a = 0, which factors to 3a(a - 3) = 0, giving the values of a as 0 and 3.

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