Question

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 = 0​

Answer 1

Answer:

m=1/24

Step-by-step explanation:

-12m×-12m=-4-2

144m= -6

m=-6/144=1/24

Answer 2

Answer:

12  and  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