Question

If the roots of $x^2 + ax + 9 = 0$ are complex, then

• A. $a<6$
• B. $a<-6$
• C. $|a|<6$
• D. $|a|>6$

Hint:

For quadratic $ax^2+bx+c=0$, roots are complex if $b^2-4ac<0$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For a quadratic equation $x^2 + ax + 9 = 0$, roots are complex if discriminant $D<0$.
Step 2: Detailed Explanation:
Discriminant $D = a^2 - 4 \times 1 \times 9 = a^2 - 36$.
For complex roots: $a^2 - 36<0 \Rightarrow a^2<36 \Rightarrow |a|<6$.
Step 3: Final Answer:
The condition is $|a|<6$.