Final answer:
To find the equation whose roots are 1/α and 1/β, we can use the sum and product of the roots of the original equation. The equation with roots x = 1/α and x = 1/β is 2x² + 3x - 6 = 0. The correct option is (a) 2x²+3x−6=0
Step-by-step explanation:
To find the equation whose roots are 1/α and 1/β, we can start by finding the sum and product of the roots of the original equation 2x²−3x−6=0. Let α and β be the roots of the equation. The sum of the roots (α+β) can be found using the formula (-b/a), where a and b are the coefficients of x² and x respectively. In this case, a=2 and b=-3, so the sum of the roots is (-(-3)/2) = 3/2.
The product of the roots (αβ) can be found using the formula (c/a), where c is the constant term of the equation. In this case, c=-6, so the product of the roots is (-6/2) = -3.
Now we can use these values to find the equation with roots 1/α and 1/β. The equation with roots x = 1/α and x = 1/β can be written as (x - 1/α)(x - 1/β) = 0. Expanding this equation, we get x² - (1/α + 1/β)x + 1/(αβ) = 0.
Since we have already calculated the sum of the roots as 3/2 and the product of the roots as -3, we can substitute these values into the equation: x² - (3/2)x - 1/(-3) = 0. Simplifying, we get 2x² + 3x - 6 = 0.
The correct option is (a) 2x²+3x−6=0