Answer:
x = 2, x = 5
Explanation:
given the quadratic equation
x² - 7x + 10 = 0
consider the factors of the constant term (+ 10) which sum to give the coefficient of the x- term (- 7 )
the factors are - 2 and - 5 , since
- 2 × - 5 = + 10 and - 2 - 5 = - 7
use these factors to split the x- term
x² - 2x - 5x + 10 = 0 ( factor the first/second and third/fourth terms )
x(x - 2) - 5(x - 2) = 0 ← factor out (x - 2) from each term
(x - 2)(x - 5) = 0
equate each factor to zero and solve for x
x - 2 = 0 ( add 2 to both sides )
x = 2
x - 5 = 0 ( add 5 to both sides )
x = 5
the zeros are x = 2 and x = 5