Question

• The roots of the quadratic equation 3x² = 5x+1 =0 are given as h and k -Find the value of h^2 -k​

Answer 1

20√37/36

Explanation:

1. Replace x with h and k in the equation:

3h² = 5h + 1 ... (Equation 1)

3k² = 5k + 1 ... (Equation 2)

2. Rearrange both equations so that one side is equal to zero:

3h² - 5h - 1 = 0

3k² - 5k - 1 = 0

3. Solve for h and k using the quadratic formula:

h = [5 ± √(5² - 43(-1))]/(2*3)

= [5 ± √37]/6

k = [5 ± √(5² - 43(-1))]/(2*3)

= [5 ∓ √37]/6

4. Find h² - k:

h² - k = ([5 + √37]/6)² - ([5 - √37]/6)

= (25 + 10√37 + 37)/36 - (25 - 10√37 + 37)/36

= 20√37/36