Question

solve the following quadrative equation............
1. find the value of 'm' if the following equation has equal roots:-
(m-2)x^2-(5+m)x+16=0

Answer 1

Answer:

(m-2) x²-(5+m) x+16=0

Comparing the above Equation with ax²+bx+c=0

a=(m-2), b=-5-m and c=16

b²-4ac=(-5-m) ²-4×(m-2) ×16

=25-2×-5×-m+m²-4×(m-2) ×16

=25+10m+m²-64(m-2)

=25+10m+m²-64m+128

.. =153-54m+m²

=m2-54m+153

But the roots are real

therefore, m²-54m+153=0

m²-51m-3m+153=0

m(m-51) -3(m-51) =0

(m-51) (m-3) =0 therefore, m=51 or3