Question

find m if (m-12)x²+2(m-12)x+2=0 has real and equal roots

Answer 1

Let the of this polynomial be A and B.
Given , A= B.
P(x)= (m-12)x^2 + 2(m-12)x +2
A+B = -b/a .
A+B = -2(m-12) / m-12 .
2A= -2[(m-12) / m-12)].
A = m-12/m-12 = 1.
A×B = c/a .
(A)^2 = 2/ m-12.
(1)^2 = 2/ m-12
1 = 2/ m-12
m-12 = 2.
m= 14.
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