Question

Example 6. Discuss the nature of the roots of the equation
(m + 6) x2 + (m + 6) x + 2 = 0.​

Answer 1

Answer:

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Answer 2

$Compare \: given \: Quadratic \: equation:$

$(m+6)x^{2} + (m+6)x + 2 = 0 \:with \\ ax^{2}+bx+c=0\: we \:get$

$a = (m+6) , b = m+6 \:and \: c = 2$

$Discreminant (D) = b^{2}-4ac$

$= (m+6)^{2} - 4 \times (m+6)\times 2$

$= (m+6)( m+6 - 8 )\\=(m+6)(m-2)$

Therefore.,

$i) If \: D \gt 0 \implies Roots \: are \: real \:and \\distinct$

$ii) If \: D = 0 \implies Roots \: are \: real \:and \\equal$

$iii) If \: D \lt 0 \implies Roots \: are \:not \: real$

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