Respuesta :
Answer:
The roots of the equation are x = [tex]\frac{3+\sqrt{151}i}{10}[/tex] and x = [tex]\frac{3-\sqrt{151}i}{10}[/tex]
and there are no real roots of the equation given above
Step-by-step explanation:
To solve:
5x² − 3x + 17 = 9
or
⇒ 5x² − 3x + 17 - 9 = 0
or
⇒ 5x² − 3x + 8 = 0
Now,
the roots of the equation in the form ax² + bx + c = 0 is given as:
x = [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
in the above given equation
a = 5
b = -3
c = 8
therefore,
x = [tex]\frac{-(-3)\pm\sqrt{(-3)^2-4\times5\times8}}{2\times5}[/tex]
or
x = [tex]\frac{3\pm\sqrt{9-160}}{10}[/tex]
or
x = [tex]\frac{3+\sqrt{-151}}{10}[/tex] and x = [tex]\frac{3-\sqrt{-151}}{10}[/tex]
or
x = [tex]\frac{3+\sqrt{151}i}{10}[/tex] and x = [tex]\frac{3-\sqrt{151}i}{10}[/tex]
here i = √(-1)
Hence,
The roots of the equation are x = [tex]\frac{3+\sqrt{151}i}{10}[/tex] and x = [tex]\frac{3-\sqrt{151}i}{10}[/tex]
and there are no real roots of the equation given above
