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