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 aboveStep-by-step explanation:To solve:5x² − 3x + 17 = 9or⇒ 5x² − 3x + 17 - 9 = 0or⇒ 5x² − 3x + 8 = 0Now,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 equationa = 5b = -3c = 8therefore,x = [tex]\frac{-(-3)\pm\sqrt{(-3)^2-4\times5\times8}}{2\times5}[/tex]orx = [tex]\frac{3\pm\sqrt{9-160}}{10}[/tex]orx = [tex]\frac{3+\sqrt{-151}}{10}[/tex] and x = [tex]\frac{3-\sqrt{-151}}{10}[/tex]orx = [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