Find the value of m if the following equation have equal roots (m-2)x+16=0
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Answer:
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Answer:
m = 3, 51
Step-by-step explanation:
Given Equation should be,
(m - 2)x² - (5 + m)x + 16 = 0
On comparing with ax² + bx + c = 0, we get
a = (m - 2), b = -(5 + m), c = 16
Equation have equal roots.
∴ D = 0
=> b² - 4ac = 0
=> [-(5 + m)]² - 4(m - 2)(16) = 0
=> 25 + m² + 10m - 4[16m - 32] = 0
=> 25 + m² + 10m - 64m + 128 = 0
=> m² - 54m + 153 = 0
=> m² - 51m - 3m + 153 = 0
=> m(m - 51) - 3(m - 51) = 0
=> (m - 3)(m - 51) = 0
=> m = 3, 51
Therefore, the value of m = 3,51
Hope it helps!
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