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Question
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
Solution
Given quadratic equation is (m + 4)x2 + (m + 1)x + 1 = 0
The quadratic equation has real and equal roots if its discriminant is zero.
`=>` D = b2 – 4ac = 0
`=>` (m + 1)2 – 4(m + 4)(1) = 0
`=>` m2 + 2m + 1 – 4m – 16 = 0
`=>` m2 – 2m – 15 = 0
`=>` m2 – 5m + 3m – 15 = 0
`=>` m(m – 5) + 3(m – 5) = 0
`=>` (m – 5)(m + 3) = 0
`=>` m = 5 or m = –3
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