Question

o produto das raizes da equaçao 8x2-9x+c=0 e igual a 3/4.calcular o valor do coeficiente c

Answer 1

Basta aplicar em bhaskara!

8x² - 9x + c = 0

Delta = b² - 4ac
Delta = (-9)² - 4 . 8 . c
Delta = 81 - 32c

$x_{1} . x_{2} = \frac{3}{4}$

Sendo:

$x_{1} = \frac{-b + \sqrt{delta} }{2a}$

$x_{2} = \frac{-b - \sqrt{delta} }{2a}$


Substituindo valores:

$x_{1} = \frac{9 + \sqrt{81-32c} }{16}$

$x_{2} = \frac{9 - \sqrt{81-32c} }{16}$

$\frac{9+ \sqrt{81-32c} }{16} . \frac{9- \sqrt{81-32c} }{16} = \frac{3}{4}$

$\frac{(9+ \sqrt{81-32c}). (9- \sqrt{81-32c}) }{256} = \frac{3}{4}$

$(9+ \sqrt{81-32c}). (9- \sqrt{81-32c}) = \frac{256 .3}{4}$

$(9+ \sqrt{81-32c}). (9- \sqrt{81-32c})= 192$

$81 - 9 \sqrt{81-32c} + 9 \sqrt{81-32c} - ( \sqrt{81-32c})^{2} = 192$

$81 - 81 + 32c = 192$

$32c = 192$

$c = \frac{192}{32}$

$c = 6$

Answer 2

8x2-9x+c=0

    x1 * x2 =   c    
                      a

     c  =    3
     8        4

           4c = 8.3
 
              4c = 24
 
                 c = 6