Question

One of the roots of the equation x^2−bx+c=0 is equal to 5. Find c in terms of b.

Answer 1

c = 5b - 25

Explanation:

Since one of the roots is equal to 5, we simply insert 5 in the quadratic equation. This means we replace the value of x with 5. We then proceed to collect like terms, rearrange the equation and make c the subject of formula

(5)^2 -5b + c = 0

25 -5b + c = 0

We then rearrange to make c the subject of formula.

c = 5b - 25

Or c = 5(b - 5)

Answer 2

c = 5b - 25

Explanation:

If

x² − bx + c = 0

where x = 5

we have

(5)² − b*(5) + c = 0

⇒ 25 - 5b + c = 0

⇒ c = 5b - 25 = 5*(b - 5)