Question

Find the zeros of the polynomial x² + 2x – 195.

Answer 1

Given: f(x) = x² + 2x – 195

Step-wise calculation:

1. Solve f(x) = 0:

x² + 2x – 195 = 0

2. Split the middle term:

Find two numbers whose product is –195 and sum is 2.

These are 15 and –13.

3. Rewrite and factor:

x² + 2x – 195 

= x² + 15x – 13x – 195 

= x(x + 15) – 13(x + 15)

= (x + 15)(x – 13)

4. Set each factor to zero:

x + 15 = 0

⇒ x = –15

x – 13 = 0 

⇒ x = 13

The zeros are x = –15 and x = 13.