Multiple choice

The sum of the roots of the equations 4x - 3 (2x+3) + 128 = 0 is _____.

  1. 5

  2. 6

  3. 7

  4. 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let 2^x = y. Then 4^x = y^2. Equation: y^2 - 3(8y) + 128 = 0 => y^2 - 24y + 128 = 0. Factors: (y-16)(y-8) = 0. So y = 16 or y = 8. 2^x = 16 => x = 4. 2^x = 8 => x = 3. Sum of roots = 4 + 3 = 7.

AI explanation

Rewrite the constants using base 2 to get 2^(2x) - 3 * 2^(x + 3) + 128 = 0. This simplifies to 2^(2x) - 24 * 2^x + 128 = 0. By substituting y = 2^x, the equation becomes a quadratic y^2 - 24y + 128 = 0. Factoring this quadratic yields (y - 16)(y - 8) = 0, giving y values of 16 and 8. Reverting to x gives 2^x = 16 and 2^x = 8, so the roots are 4 and 3, and their sum is 7.

Keep practicing — related questions