# Quadratic Equations · Mathematics · AP EAPCET

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AP EAPCET 2022 - 4th July Morning Shift
If $$f(x)=a x^2+b x+c$$ for some $$a, b, c \in R$$ with $$a+b+c=3$$ and $$f(x+y)=f(x)+f(y)+x y, \forall x, y \in R$$. Then, $$\sum_\limits{n=1}^{10} f... AP EAPCET 2022 - 4th July Morning Shift The number of positive real roots of the equation$$3^{x+1}+3^{-x+1}=10$$is AP EAPCET 2022 - 4th July Morning Shift The number of real roots of the equation$$\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}=\frac{13}{6}$$is AP EAPCET 2021 - 20th August Morning Shift If$$\alpha$$and$$\beta$$are the roots of the quadratic equation$$x^2+x+1=0$$, then the equation whose roots are$$\alpha^{2021}, \beta^{2021}$$i... AP EAPCET 2021 - 20th August Morning Shift If$$2, 1$$and$$1$$are roots of the equation$$x^3-4 x^2+5 x-2=0$$, then the roots of$$\left(x+\frac{1}{3}\right)^3-4\left(x+\frac{1}{3}\right)^2+...
AP EAPCET 2021 - 20th August Morning Shift
If $$f(x)=2x^3+mx^2-13x+n$$ and 2, 3 are the roots of the equation $$f(x)=0$$, then the values of m and n are
AP EAPCET 2021 - 19th August Evening Shift
If $$\alpha$$ and $$\beta$$ are the roots of $$11 x^2+12 x-13=0$$, then $$\frac{1}{\alpha^2}+\frac{1}{\beta^2}$$ is equal to (approximately close to)...
AP EAPCET 2021 - 19th August Evening Shift
The value of $$a$$ for which the equations $$x^3+a x+1=0$$ and $$x^4+a x^2+1=0$$ have a common root is
AP EAPCET 2021 - 19th August Evening Shift
If $$a$$ is a positive integer such that roots of the equation $$7 x^2-13 x+a=0$$ are rational numbers, then the smallest possible value of $$a$$ is...
AP EAPCET 2021 - 19th August Morning Shift
The sum of the roots of the equation $$e^{4 t}-10 e^{3 t}+29 e^{2 t}-22 e^t+4=0$$ is
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