A parallelogram has base (2x - 1) metres and height (4x - 7) metres. The area of the parallelogram is 1 m?.
(1) Show that 4x? - 9x + 3 = 0.
Answer (a)(i)
(*) Solve the equation 4x² – 9x + 3 = 0.
Show all your working and give your answers correct to 2 decimal places.

0.4069 ; 1.843

Step-by-step explanation:

Given:

Base of parallelogram, b = (2x - 1)

Height = (4x - 7)

Area = 1

Area of parallelogram = Base * height

Area of parallelogram = (2x - 1) * (4x - 7)

(2x - 1) * (4x - 7) = 1

8x² - 14x - 4x + 7 = 1

8x² - 18x + 7 - 1 = 0

8x² - 18x + 6 = 0

Divide through by 2

4x² - 9x + 3 = 0

Solving the quadratic equation :

Using the formula

-b ± √(b² - 4ac) / 2a

a = 4 ; b = - 9 ; c = 3

Plugging in the values :

-(-9) ± √((-9)² - 4(4)(3)) / 2(4)

9 ± √(81 - 48) / 8

9 ± √33 / 8

(9 ± 5.7445626) / 8

(9 - 5.7445626) / 8) = 0.4069

(9 + 5.7445626) / 8 = 1.843

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