Question

Find the value of m for which mx^2 - 6x + 5 = 0 has one solution.

Answer 1

m =
`(9)/(5)`

Explanation:

Given a quadratic equation in standard form ax² + bx + c = 0 ( a ≠ 0)

Then the discriminant Δ = b² - 4ac gives information on the nature of the solutions.

For the equation to have 1 solution we require b² - 4ac = 0

mx² - 6x + 5 = 0 ← is in standard form

with a = m, b = - 6, c = 5, then

b² - 4ac = 0

(- 6)² - (4 × m × 5) = 0

36 - 20m = 0 ( subtract 36 from both sides )

- 20m = - 36 ( divide both sides by - 20 )

m =
`(-36)/(-20)` =
`(9)/(5)`