List of top Mathematics Questions on System of Linear Equations asked in TS EAMCET

A quadratic equation \[ x^2-ax+b=0,\qquad a>0 \] has real roots. If the sum of the roots is less than the product of the roots, then \(b\) lies in the interval

When each root of the equation \[ x^3-ax^2+bx+1=0 \] is diminished by \(h\), if the transformed equation takes the form \[ 9x^3+\left(9+\frac{a^3}{3}\right)=0, \] then \(ah=\)

If \(a\in \mathbb{Z}\) and the equation \[ (x-a)(x-10)+1=0 \] has integral roots, then the values of \(a\) are:

The number of real roots of the equation \[ x^7+3x^5-13x^3-15x=0 \] is:

If \(\alpha,\beta\) are the rational roots and \(l,m\) are the irrational roots of \[ (x^2-9x+11)^2-(x-4)(x-5)=3, \] then \(\alpha+\beta+lm=\)

If $2x^5+ax^4-12x^3+bx^2+x+c=0$ is reciprocal equation of class one, find sum of rational roots.

If \(\alpha,\beta,5\) are the roots of the equation \[ x^3-ax+a= \frac{\sin^2x+\cos^4x} {\cos^2x+\sin^4x}, \] then \(a(\alpha+\beta)=\)

If the system of equations \[ ax+y-2z=3,\qquad 2x-y+3z=b,\qquad x+2y-z=3 \] has infinitely many solutions, then \(3a-2b=\)

If $\alpha,\beta,\gamma$ are roots of $x^3-ax^2-4x+4a=0$ with $\alpha+\beta=0$, $\beta+\gamma=5$, find sum of all possible $a$.

If 2 and 3 are the two roots of the equation \[ 2x^3 + mx^2 - 13x + n = 0, \] then the values of \(m, n\) are respectively

Let \(\alpha,\beta,\gamma,\delta\) be the roots of \[ 4x^4+8x^3-17x^2-12x+9=0. \] If \[ 4(\alpha+4)(\beta+4)(\gamma+4)(\delta+4)=k, \] then \(k=\)

If the minimum value of $ax^2-7x+3a$ is $-\frac{1}{8}$, find sum of roots of $ax^2-7x+3a=0$.}

If $\alpha,\beta$ are roots of $2x^2-x-3\lambda=0$ and $\alpha,\gamma$ are roots of $2x^2+9x+2\lambda=0$, find equation of roots $2\alpha+\beta$ and $\beta+\gamma$.

If the equations \[ ax^2+2bx+3c=0,\qquad 3x^2+8x+15=0 \] have a common root, where \(a,b,c\) are sides of triangle \(ABC\), then \[ \cos2A+\cos2B+\cos2C= \]

If the system \[ x+y-z=\lambda, \] \[ 2x-y+\mu z=2, \] \[ x-y+3z=1 \] is inconsistent, then

If the system of equations \[ x + y + z = 1,\quad x + 2y + 4z = K,\quad x + 4y + 10z = K^2 \] is consistent, then \(K =\)

If the system of simultaneous linear equations \(x - 2y + z = 0\), \(2x + 3y + z = 6\) and \(x + 2y + pz = q\) has infinitely many solutions, then

If both roots of the equation $x^2 - 5ax + 6a = 0$ exceed 1, then the range of 'a' is

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4 - 4x^3 + 3x^2 + 2x - 2 = 0$ such that $\alpha$ and $\beta$ are integers and $\gamma, \delta$ are irrational numbers, then $\alpha + 2\beta + \gamma^2 + \delta^2 =$

The equation having the multiple root of the equation $x^4 + 4x^3 - 16x - 16 = 0$ as its root is

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $12x^4-56x^3+89x^2-56x+12=0$ such that $\alpha\beta = \gamma\delta = 1$ and $\frac{\alpha+\beta}{\gamma+\delta}>1$, then $\frac{\alpha+\beta}{\gamma+\delta} =$

If $1+2i$ is a root of the equation $x^4 - 3x^3 + 8x^2 - 7x + 5 = 0$, then sum of the squares of the other roots is

Sum of all the roots of the equation $||2x-3|-4| = 2$ is

If $\tan\theta$ and $\cot\theta$ are two distinct roots of the equation $ax^2+bx+c=0, a\neq0, b\neq0$, then

If the equations $x^2 + px + 2 = 0$ and $x^2 + x + 2p = 0$ have a common root then the sum of the roots of the equation $x^2 + 2px + 8 = 0$ is