This biology question covers important biological concepts and processes. The step-by-step explanation below helps you understand the underlying mechanisms and reasoning.
ScanSolve AI Answer
Let's find the quadratic equation from its roots. Step 1: Identify the given roots. The roots are r_1 = (5)/(4) and r_2 = (3)/(2). Step 2: Calculate the sum of the roots. Sum = r_1 + r_2 = (5)/(4) + (3)/(2) To add these fractions, find a common denominator, which is 4. Sum = (5)/(4) + (3 × 2)/(2 × 2) = (5)/(4) + (6)/(4) = (5+6)/(4) = (11)/(4) Step 3: Calculate the product of the roots. Product = r_1 × r_2 = (5)/(4) × (3)/(2) Product = (5 × 3)/(4 × 2) = (15)/(8) Step 4: Form the quadratic equation using the formula x^2 - (sum of roots)x + (product of roots) = 0. Substitute the sum and product into the formula: x^2 - ((11)/(4))x + ((15)/(8)) = 0 Step 5: Clear the denominators to obtain an equation with integer coefficients. Multiply the entire equation by the least common multiple (LCM) of the denominators (4 and 8), which is 8. 8 (x^2 - (11)/(4)x + (15)/(8)) = 8 × 0 8x^2 - (8 × (11)/(4))x + (8 × (15)/(8)) = 0 8x^2 - (2 × 11)x + 15 = 0 8x^2 - 22x + 15 = 0 The equation is 8x^2 - 22x + 15 = 0. 3 done, 2 left today. You're making progress.