if α,β are the roots of x^2-3x+a=0 and a ∈ R and α

Question

if α,β are the roots of x^2-3x+a=0 and a ∈ R and α<1<β then 
a. a∈(-infinity,2)
b.a∈(-infinity,9/4)
c.a∈(2,9/4)

anonymous · Answer

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anonymous · Answer

Clearly, alpha + beta = 3
alpha * beta = a

anonymous · Answer

9 -4a>=0

anonymous · Answer

Option (b)

anonymous · Answer

put f(1)<0 coz parabola is upward dirn

anonymous · Answer

@samigupta8 , is the option(b) correct? 9/4 should be in closed interval...

anonymous · Answer

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samigupta8 · Answer

i didn't undrstand why u took f(1)<0

samigupta8 · Answer

@hartnn pls..luk over here

samigupta8 · Answer

@AllTehMaffs pls..hlp

hartnn · Answer

since x^2-3x+a=0 means parabola is upward opening (as a>0) , right ?
also it says that 1 root is <1 and other root is >1 so, (1,0) will lie in between roots,
thats how divu drew that diagram, did you get it now ?
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