Question

In each of the examples given below, determine whether the values given against each of the quadratic equations are the roots of the equation or not. x² - 4x + 3 = 0; x = 1, 2, 3​

Answer 1

x = 1, 3

Explanation:

x² - 4x + 3 = 0 ← quadratic equation in standard form

consider the factors of the constant term (+ 3) which sum to give the coefficient of the x- term (- 4)

the factors are - 1 and - 3 , since

- 1 × - 3 = + 3 and - 1 - 3 = - 4

use these factors to split the x- term

x² - x - 3x + 3 = 0 ( factor the first/second and third/fourth terms )

x(x - 1) - 3(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(x - 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ( add 1 to both sides )

x = 1

x - 3 = 0 ( add 3 to both sides )

x = 3

the roots of the equation are x = 1 , 3