Question

If \( b^2 \geq 4ac \) for the equation \( ax^4 + bx^2 + c = 0 \), then all the roots of the equation will be real if

• A. \( b>0, a<0, c>0 \)
• B. \( b>0, a>0, c>0 \)
• C. \( b>0, a>0, c<0 \)
• D. \( b = 0, a>0, c>0 \)

Hint:

Check the discriminant of the quadratic equation for the condition of real roots.

Answer 1

The Correct Option is C

Step 1: Condition for real roots.
For the quartic equation \( ax^4 + bx^2 + c = 0 \), real roots exist when \( b^2 - 4ac \geq 0 \), and we examine the conditions for the discriminant.

Step 2: Conclusion.
Thus, the correct answer is option (C).

Final Answer: \[ \boxed{\text{(C) } b>0, a>0, c<0} \]