3) If the roots of the given quadratic equation are real and equal then find
the value of m’.
(m-12) x² + 2 (m-12) x + 2

2 thoughts on “3) If the roots of the given quadratic equation are real and equal then find<br />the value of m’.<br />(m-12) x² + 2 (m-12) x + 2”

1. [tex]\sf Equal \: and \: real \: roots \: ⇒b² – 4ac = 0 [/tex]

   [tex]\sf \therefore b² = 4ac[/tex]

   [tex]\sf \: a=(m−12),b=2(m−12),c=2[/tex]

   [tex]\sf [2(m−12)] {}^{2} =4(m−12)(2)[/tex]

   [tex]\sf4(m−12) {}^{2} =4(m−12)(2)[/tex]

   [tex]\sf (m−12) {}^{2} −2(m−12)=0[/tex]

   [tex]\sf(m−12)(m−12−2)=0 [/tex]

   [tex]\sf∴m=14,12[/tex]

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2. Answer:

   14

   Step-by-step explanation:

   To roots to be real and equal, discriminant of the equation must be 0.

   Discriminant of ax² + bx + c = 0 is given by b² – 4ac. On comparing,

   a = (m – 12), b = 2(m – 12), c = 2

   ⇒ discriminant = 0

   ⇒ [2(m – 12)]² – 4(2)(m – 12) = 0

   ⇒ 4(m – 12)² – 8(m – 12) = 0

   ⇒ 4(m – 12)[ (m – 12) – 2 ] = 0

   ⇒ 4(m – 12)(m – 14) = 0

   ⇒ m – 12 = 0 or m – 14 = 0

   ⇒ m = 12 or m = 14

   But for m = 12, (m – 12)x² + 2(m – 12) + 2 = 0 is not true.

   m = 14 must be preferred

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