If √5 and −√5 are two zeroes of the polynomial x³ + 3x² − 5x − 15, find its third zero

Video Explanation

Watch the video explanation below:

Given

f(x) = x³ + 3x² − 5x − 15

Two zeroes of the polynomial are:

√5 and −√5

To Find

The third zero of the polynomial.

Solution

Let the third zero be α.

For a cubic polynomial:

Sum of zeroes = −(coefficient of x²)/(coefficient of x³)

= −3/1 = −3

Step 1: Use the Sum of Zeroes

√5 + (−√5) + α = −3

0 + α = −3

α = −3

Final Answer

The third zero of the polynomial is:

−3

Correct Option

(b) −3

Conclusion

Hence, if √5 and −√5 are two zeroes of the polynomial x³ + 3x² − 5x − 15, then its third zero is −3.