The zeroes of the quadratic polynomial x² + 99x + 127 are

Video Explanation

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Given

Quadratic polynomial: f(x) = x² + 99x + 127

To Find

The nature of the zeroes of the given polynomial.

Solution

For a quadratic polynomial ax² + bx + c:

• Sum of zeroes = −b/a
• Product of zeroes = c/a

Step 1: Identify a, b and c

a = 1,   b = 99,   c = 127

Step 2: Find the Sum and Product of Zeroes

Sum of zeroes = −b/a = −99

Product of zeroes = c/a = 127

Step 3: Determine the Nature of Zeroes

Since:

• Sum of zeroes is negative, and
• Product of zeroes is positive

Both zeroes must be negative.

Final Answer

The zeroes of the given polynomial are:

both negative

Correct Option

(b) both negative

Conclusion

Hence, the zeroes of the quadratic polynomial x² + 99x + 127 are both negative.