Final answer:
To find the product of the solutions 'a' and 'b' of the given equation x² - 10x = 39, we can use the quadratic formula to find the solutions for x. Once we have the solutions, we can multiply them to find the product 'a × b'. The product is approximately -2.02 × 12.02 ≈ -24.3, so the correct answer is (b) -29.
Step-by-step explanation:
To find the product of the solutions, we need to determine the values of 'a' and 'b' which represent the solutions of the equation. The given equation is x² - 10x = 39. To solve this equation, we can rearrange it to the form x² - 10x - 39 = 0. We can then use the quadratic formula to find the solutions:
x = (-b ± √(b² - 4ac))/(2a)
For our equation, a = 1, b = -10, and c = -39. Substituting these values into the quadratic formula, we get x = (-(-10) ± √((-10)² - 4*(1)*(-39)))/(2*(1)). Simplifying this further, we get x = (10 ± √(100 + 156))/2. This gives us two possible solutions for x: x₁ ≈ 12.02 and x₂ ≈ -2.02. Therefore, the values of 'a' and 'b' are approximately 12.02 and -2.02, and their product 'a × b' is approximately -2.02 × 12.02 ≈ -24.3. Therefore, the correct answer is (b) -29.