establish a relation between m and n if the equation mx²-x+n =0 has real roots
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Answer:
For no real roots, the condition is D<0
So, b2−4ac<0
For the equation mx2−(m+1)x+(2m−1)=0,
a=m , b=(m+1) and c=(2m−1)
So,
(m+1)2−4×m×(2m−1) <0
(m2+1+2m)−8m2+4m<0
−7m2+6m+1 < 0
7m2−7m+m−1 > 0
7m(m−1)+1(m−1)>0
(7m+1)(m−1)>0
So, m<7−1 and m>1
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