Ex 3.6
6. find the area enclosed between the curve y= -2x²-5x+3 and the x-axis
2 answers:
Y = -2x² - 5x + 3
-2x² - 5x + 3 = 0
x = <u>-(-5) +/- √(-5² - 4(-2)(3))</u>
2(-2)
x = <u>5 +/- √(25 + 24)</u>
-4
x = <u>5 +/- √39
</u> -4<u>
</u>x = <u>5 +/- 6.244997998398398
</u> -4<u>
</u>x = <u>5 + 6.244997998398398 </u> x = <u>5 - 6.244997998398398</u>
-4 -4<u>
</u>x = <u>11.624997998398398</u> x = <u>-1.244997998398398
</u> -4 -4<u>
</u>x = -2.8112494995996 x = 0.3112494995996<u>
</u>-----------------------------------------------------------------------------------------------
y = -2x² - 5x + 3 y = -2x² - 5x + 3
y = -2(-3)² - 5(-3) + 3 y = -2(0.3)² - 5(0.3) + 3
y = -2(9) + 15 + 3 y = -2(0.09) - 0.15 + 3
y = -18 + 15 + 3 y = -0.18 - 0.15 + 3
y = -3 + 3 y = -0.33 + 3
y = 0 y = 2.67
-----------------------------------------------------------------------------------------------
(x, y) = (-3, 0) (x, y) = (0.3, 2.67)
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