Respuesta :
Answer:
b = 0.4899
Step-by-step explanation:
Given;
2(2x-1)=5x²
4x - 2 = 5x²
5x² - 4x + 2 = 0
this is a quadratic equation with;
a = 5, b = -4 and c = 2
[tex]x = \frac{-b \ \ + /-\ \ \sqrt{b^2 - \ 4ac} }{2a} \\\\x = \frac{-(-4) \ \ + /-\ \ \sqrt{(-4)^2 - \ 4(5*2)} }{2(5)} \\\\x = \frac{4 \ \ + /-\ \ \sqrt{16 - \ 40} }{10} \\\\x = \frac{4 \ \ + /-\ \ \sqrt{-24} }{10}\\\\x = \frac{4 \ \ +/-\ \ (\sqrt{24)} (\sqrt{-1} ) }{10} \\\\x = \frac{4 \ \ +/-\ \ (\sqrt{24)} (i )}{10}\\\\ x = \frac{4 \ \ +/-\ \ (4.899) (i )}{10}\\\\ x = \frac{4 \ \ +\ \ (4.899) (i )}{10} \ \ or \ \ x = \frac{4 \ \ -\ \ (4.899) (i )}{10}\\\\[/tex]
in terms of a + bi, it will be simplified as;
[tex]x = \frac{4}{10} + \frac{(4.899) (i)}{10} \\\\x = 0.4 + 0.4899i[/tex]
Therefore, b = 0.4899
When the given expression is expressed in the simplest form of [tex]a+bi[/tex] then the value of b is 0.4899.
Given-
The given expression in the problem is,
[tex]2(2x-1)=5x^2[/tex]
Simplify this,
[tex]4x-2=5x^2[/tex]
Arrange the above equation,
[tex]5x^2-4x+2=0[/tex]
Compare the above equation with general quadratic equation,
[tex]ax^2+bx+c=0[/tex]
we get,
[tex]a=5[/tex]
[tex]b=-4[/tex]
[tex]c=2[/tex]
Find the roots of the [tex]x[/tex] . The formula to find the roots of a quadratic equation can be given as,
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4\times5\times2} }{2\times 5}[/tex]
[tex]x=\dfrac{4\pm\sqrt{16-40} }{10}[/tex]
[tex]x=\dfrac{4\pm\sqrt{-24} }{10}[/tex]
[tex]x=\dfrac{4\pm\sqrt{-24}\sqrt{-1} }{10}[/tex]
[tex]x=\dfrac{4\pm 4.899i} {10}[/tex]
Take positive sign we get,
[tex]x=\dfrac{4+ 4.899i} {10}[/tex]
Take negative sign we get,
[tex]x=\dfrac{4-4.899i} {10}[/tex]
Compare the simplified form of [tex]a+bi[/tex] with the root of [tex]x[/tex]
[tex]x=0.4+ 0.4899i[/tex]
here,
[tex]b=0.4899[/tex]
Hence when the given expression is expressed in the simplest form of [tex]a+bi[/tex] then the value of b is 0.4899.
For more about the quadratic equation follow the link below-
https://brainly.com/question/2263981
