Use the discriminant to describe the roots of each equation. Then select the best description?x^2-5x-4=0double rootReal and irrational rootReal and rational rootImaginary root

Answer:The roots are real and irrational Step-by-step explanation:* Lets explain what is the discriminant- In the quadratic equation ax² + bx + c = 0, the roots of the  equation has three cases:1- Two different real roots2- One real root or two equal real roots3- No real roots means imaginary roots- All of these cases depend on the value of a , b , c∵ The rule of the finding the roots is    x = [-b ± √(b² - 4ac)]/2a- The effective term is √(b² - 4ac) to tell us what is the types of the root# If the value under the root b² - 4ac positive means greater than 0∴ There are two different real roots# If the value under the root b² - 4ac = 0∴ There are two equal real roots means one real root# If the value under the root b² - 4ac negative means smaller than 0∴ There is real roots but the roots will be imaginary roots∴ We use the discriminant to describe the roots* Lets use it to check the roots of our problem∵ x² - 5x - 4 = 0∴ a = 1 , b = -5 , c = -4∵ Δ = b² - 4ac∴ Δ = (-5)² - 4(1)(-4) = 25 + 16 = 41 ∵ 41 > 0∴ The roots of the equation are two different real roots∵ √41 is irrational number∴ The roots are real and irrational* Lets check that by solving the equation∵ x = [-(-5) ± √41]/2(1) = [5 ± √41]/2∴ x = [5+√41]/2 , x = [5-√41]/2 ⇒ both real and irrational