Doubt from Quadratic equation

#1

please somebody solve it step by step

#2

#3

Maximum value of \sin x+\cos x is \sqrt{2}

And Minimum value of y^2-y+a is \displaystyle a-\frac{1}{4}.

So for No real Solution, We have

\displaystyle \Rightarrow a-\frac{1}{4}>\sqrt{2}\Rightarrow a>\sqrt{2}+\frac{1}{4}.

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#4

Yess, sorry, i took the numerator as root D instead of D

Thank you @Jagdish_Singh sir