Multiple choice

A quadratic equation $a{ x }^{ 2 }+bx+c=0$ has no real roots if:

  1. ${ b }^{ 2 }-4ac=0$
  2. ${ b }^{ 2 }> 4ac$
  3. ${ b }^{ 2 }< 4ac$
  4. ${ b }^{ 2 }+4ac=0$
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C Correct answer
Explanation

A quadratic equation has no real roots if the discriminant (b^2 - 4ac) is less than zero.

AI explanation

The discriminant of a quadratic equation determines the nature of its roots based on the value $b^2 - 4ac$. If the discriminant is strictly less than zero, the square root of a negative number is required, yielding complex numbers instead of real numbers. Therefore, the condition for no real roots is $b^2 < 4ac$. The condition is $b^2 < 4ac$.

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