Question

If the equation mx² + 2x + m = 0 is satisfied by only one real value of x, then the values of m are ______ and ______.

Answer 1

If the equation mx² + 2x + m = 0 is satisfied by only one real value of x, then the values of m are –1 and 1.

Explanation:

For m ≠ 0 the equation is quadratic; require discriminant = 0 for a single (repeated) real root:

4 – 4m² = 0

⇒ m² = 1

⇒ m = ±1

Remark: m = 0 gives 2x = 0 ⇒ x = 0, a single solution, but then the equation is linear rather than quadratic, so typical answers for the quadratic case are m = –1 and m = 1.