Multiple choice

Which of the following equations has two distinct real roots ?

  1. $2x^2-3\sqrt 2 x+\dfrac 94=0$
  2. $x^{2}+x-5=0$
  3. $x^{2}+3x+2\sqrt{2}=0$
  4. $5x^{2}-3x+1=0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A quadratic equation has two distinct real roots if its discriminant D = b^2 - 4ac > 0. For B, x^2 + x - 5 = 0, D = 1^2 - 4(1)(-5) = 21, which is greater than 0.

AI explanation

A quadratic equation has two distinct real roots when its discriminant is greater than zero. For x squared plus x minus 5 equals 0, the discriminant is 1 squared minus 4 times 1 times negative 5, which equals 1 plus 20, giving 21. Since 21 is greater than 0, the equation has two distinct real roots.

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