Multiple choice

The arrangement of the following quadratic equations in the descending order of their sum of the roots. A: $ x^{2}+11=0$ B: $(x+2) (x-3) =0$ C: $5x^{ 2 }+4x=0$ D: $2x^{ 2 }+3x-5=0$

  1. $A,B,C,D$
  2. $D,C,B,A$
  3. $B,A,C,D$
  4. $A,C,B,D$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sum of roots for ax^2 + bx + c = 0 is -b/a. A: x^2 + 11 = 0, sum = 0. B: x^2 - x - 6 = 0, sum = 1. C: 5x^2 + 4x = 0, sum = -4/5 = -0.8. D: 2x^2 + 3x - 5 = 0, sum = -3/2 = -1.5. Descending order: B(1) > A(0) > C(-0.8) > D(-1.5).

AI explanation

Use the relationship between roots and coefficients where the sum of the roots of a quadratic equation equals negative b divided by a. The sums of the roots for the four equations are 0 for A, 1 for B, negative 4 divided by 5 for C, and negative 3 divided by 2 for D. Arranging these values in descending order gives 1, 0, negative 4 divided by 5, and negative 3 divided by 2. The result is B, A, C, D.