Multiple choice

Arrange of the following quadratic equations in the ascending order of their number of real roots: A: $x^{2}-5x+6=0$ B: $x^{2}-7|x|=0$ C: $x^{2}-4x+5=0$ D: $x^{2}-5|x|+6=0$

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

A: x^2 - 5x + 6 = 0 has 2 roots (x=2, 3). B: x^2 - 7|x| = 0 has 3 roots (x=0, 7, -7). C: x^2 - 4x + 5 = 0 has 0 real roots (discriminant < 0). D: x^2 - 5|x| + 6 = 0 has 4 roots (x=2, -2, 3, -3). Ascending order: C(0), A(2), B(3), D(4).

AI explanation

Equation C has a negative discriminant (16 - 20 = -4), giving it zero real roots. Equation A factors into (x-2)(x-3)=0, yielding two real roots. Equations B and D involve absolute values, meaning we solve for both positive and negative x; equation B yields three real roots (x = -7, 0, 7), while equation D yields four real roots (x = -3, -2, 2, 3). Arranging them in ascending order of their number of real roots gives the sequence C, A, B, D.

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