Doubt from quadratic equations

Is it D?

how ur last condition of taking range implies that
their will be one root????
@Abhishek_2020_5

I have reached to the linear equation in 't' by simplifying the original equation. So, I found the roots of the initial equation only, but in terms of 't'. In the final step I just put the condition on the roots.

as t is parabola nd if u will rhs side is hyperbola type after more simplification how u can prove their will be one root in this interval
u have taken full interval of range their may be chance when it will cut graph at no point or may be in more point too..

@Hari_Shankar sir any shortcut approch u find???

If you don't get it, you can just put x(x+1) in place of 't'. then you'll get a quadratic in 'x' and then you can apply D>=0 to get interval of 'a'. Which will be enough to show atleast 1 real root.

See Question no. (10)

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thanks jagdish sir...

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