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Use the Zero Product Property to find the x-intercepts for y=3x2−7x+4

User Moljac
by
8.3k points

1 Answer

3 votes

Answer:

x =
(4)/(3), x = 1

Explanation:

To find the x- intercepts, let y = 0 , that is

3x² - 7x + 4 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × 4 = 12 and sum = - 7

The factors are - 3 and - 4

Use these factors to split the x- term

3x² - 3x - 4x + 4 = 0 ( factor the first/second and third/fourth terms )

3x(x - 1) - 4(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(3x - 4) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

3x - 4 = 0 ⇒ 3x = 4 ⇒ x =
(4)/(3)

x- intercepts are x =
(4)/(3) , x = 1

(
(4)/(3), 0 ), (1, 0 ) ← in coordinate form

User Mick Walker
by
7.7k points

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