Question

If the zeroes of the quadratic polynomial \(ax^2+bx+c \  (c≠0)\) are equal, then

• A. c and a have opposite signs
• B. c and a have same signs
• C. \(b^2≠4ac\)
• D. None of these

Answer 1

The Correct Option is B

Given the quadratic polynomial ax² + bx + c (c ≠ 0) with equal zeroes.

For a quadratic polynomial to have equal zeroes, its discriminant must be zero:

Discriminant (D) = b² - 4ac = 0

This implies: b² = 4ac

Now considering the product of roots (αα = α²):

Product of roots = c/a = α²

Since c ≠ 0 and α² > 0 (as squares are always positive for real numbers), we conclude:

• c/a must be positive
• This means c and a must have the same sign

Analyzing the options:

1. c and a have opposite signs → False
2. c and a have the same signs → True
3. b² ≠ 4ac → False (as b² = 4ac for equal roots)
4. None of these → False

Therefore, the correct answer is: (2) c and a have the same signs