List of top Mathematics Questions on Quadratic Equations asked in AP EAPCET

If the equation \[ 2x^2-5x+k=0 \] has equal roots, then the value of \(k\) is

If \(\alpha,\beta\) are the roots of the quadratic equation \[ x^2-3x+1=0, \] then the value of \(\alpha^3+\beta^3\) is:

Let \(\alpha\) and \(\beta\) be the roots of \[ x^2+bx+c=0. \] If \[ \alpha^2+\beta^2=14 \] and \[ \alpha\beta=3, \] then the value of \(b^2\) is:

If \(a\), \(b\), \(c\), \(d\) are real numbers such that \[ a\lt b\lt c\lt d, \] then the roots of the equation \[ (x-a)(x-c)+2(x-b)(x-d)=0 \] are

If one root of the quadratic equation \[ ax^2+bx+c=0 \] is equal to the \(n^{th}\) power of the other, then \[ (ac^n)^{\frac{1}{n+1}}+(a^nc)^{\frac{1}{n+1}}= \]

The sum of squares of roots of the equation \[ x^{\frac{2}{3}}+x^{\frac{1}{3}}-2=0 \] is

If \(f(x)=ax^2+bx+c\) satisfies \[ f(1)+2f(2)=0 \] and \[ 2f(1)+f(2)=0, \] then \(3a+b=\)

\(\alpha,\beta\) are the roots of \[ x^2-10x-8=0 \] with \(\alpha\gt \beta\). If \[ a_n=\alpha^n-\beta^n \] for \(n\in \mathbb{N}\), then the value of \[ \frac{a_{10}-8a_8}{5a_9} \] is:

The number of real values of \(m\) so that the equation \[ x^2+(2m+1)x+m=0 \] has equal roots is:

If \[ S=\{m\in \mathbb{R}:x^2-2(1+3m)x+7(3+2m)=0 \text{ has distinct roots}\}, \] then the number of elements in \(S\) is

If the difference between the roots of \[ x^2+ax+b=0 \] and that of the roots of \[ x^2+bx+a=0 \] is same and \(a\neq b\), then

For what values of \(a \in \mathbb{Z}\), the quadratic expression \[ (x+a)(x+1991)+1 \] can be factorised as \[ (x+b)(x+c), \] where \(b,c \in \mathbb{Z}\)?

If \[ f(f(0))=0, \] where \[ f(x)=x^2+ax+b,\qquad b\neq0, \] then \(a+b=\)

The sum of the real roots of the equation \[ |x-2|^2+|x-2|-2=0 \] is