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

Video Explanation

Watch the video explanation below:

Given

f(x) = x³ + x² − 5x − 5

Two zeros of the polynomial are:

√5 and −√5

To Find

The third zero of the polynomial.

Solution

Let the three zeros of the polynomial be:

√5, −√5 and α

For a cubic polynomial:

x³ + x² − 5x − 5

Sum of the zeros = −(coefficient of x²)/(coefficient of x³)

= −1/1 = −1

Step 1: Use the Sum of Zeros

√5 + (−√5) + α = −1

0 + α = −1

α = −1

Final Answer

The third zero of the polynomial is:

−1

Correct Option

(b) −1

Conclusion

Hence, if two zeros of the polynomial x³ + x² − 5x − 5 are √5 and −√5, then its third zero is −1.