Mathematics
For the equation given below, find the value of 'm' so that the equation has equal roots. Also, find the solution of the equation :
3x2 + 12x + (m + 7) = 0
Quadratic Equations
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Answer
Since, equation has equal roots, D = 0.
∴ b2 - 4ac = 0
⇒ (12)2 - 4(3)(m + 7) = 0
⇒ 144 - 12(m + 7) = 0
⇒ 144 - 12m - 84 = 0
⇒ 12m = 60
⇒ m = 5.
Substituting m = 5 in 3x2 + 12x + (m + 7) = 0 we get,
⇒ 3x2 + 12x + (m + 7) = 0
⇒ 3x2 + 12x + (5 + 7) = 0
⇒ 3x2 + 12x + 12 = 0
⇒ 3x2 + 6x + 6x + 12 = 0
⇒ 3x(x + 2) + 6(x + 2) = 0
⇒ (3x + 6)(x + 2) = 0
⇒ (3x + 6) = 0 or (x + 2) = 0
⇒ 3x = -6 or x = -2
⇒ x = -2 or x = -2.
Hence, m = 5 and x = -2.
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