Question

If one zero of the polynomial x² – 5x – c is (–1), find the value of c. Also, find the other zero.

Answer 1

1. Find the value of c

Since (–1) is a zero of the polynomial p(x) = x² – 5x – c, it must satisfy the equation p(–1) = 0.

(–1)² – 5(–1) – c = 0

1 + 5 – c = 0

6 – c = 0

c = 6

2. Find the other zero

With c = 6, the polynomial becomes p(x) = x² – 5x – 6. To find the zeros, we set the polynomial to zero and factorise it:

x² – 5x – 6 = 0

(x – 6)(x + 1) = 0

Each factor to zero gives:

x – 6 = 0

⇒ x = 6

x + 1 = 0

⇒ x = –1

Alternatively, using the sum of zeros formula for a quadratic ax² + bx + c:

Sum of zeroes = `(-b)/a`

Let the other zero be β.

`-1 + β = (-(-5))/1`

–1 + β = 5

β = 6

The value of c is 6 and the other zero of the polynomial is 6.