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Which factorizations can be used to identify the real zeros of the function f(x) = -20x^2 + 23x - 6 ?

1 Answer

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Answer:

see explanation

Explanation:

To find the zeros equate f(x) to zero, that is

- 20x² + 23x - 6 = 0 ( multiply through by - 1 )

20x² - 23x + 6 = 0

To factorise the quadratic

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

product = 20 × 6 = 120 and sum = - 23

The factors are - 15 and - 8

Use these factors to split the x- term

20x² - 15x - 8x + 6 = 0 ( factor the first/second and third/fourth terms )

5x(4x - 3) - 2(4x - 3) = 0 ← factor out (4x - 3)

(4x - 3)(5x - 2) = 0

Equate each factor to zero and solve for x

4x - 3 = 0 ⇒ 4x = 3 ⇒ x =
(3)/(4)

5x - 2 = 0 ⇒ 5x = 2 ⇒ x =
(2)/(5)

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