Consider the following two statements
$I$. Any pair of consistent liner equations in two variables must have a unique solution.
$II$. There do not exist two consecutive integers, the sum of whose squares is $365$.Then,
both $I$ and $II$ are true
both $I$ and $II$ are false
$I$ is true and $II$ is false
$I$ is false and $II$ is true
Two distinct polynomials $f(x)$ and $g(x)$ are defined as follows:
$f(x)=x^2+a x+2 ; g(x)=x^2+2 x+a$.If the equations $f(x)=0$ and $g(x)=0$ have a common root, then the sum of the roots of the equation $f(x)+g(x)=0$ is
Let $a, b, c, d$ be real numbers between $-5$ and $5$ such that $|a|=\sqrt{4-\sqrt{5-a}},|b|=\sqrt{4+\sqrt{5-b}},|c|=\sqrt{4-\sqrt{5+c}}$ $|d|=\sqrt{4+\sqrt{5+d}}$ Then, the product $a b c d$ is
The roots of the equation $4{x^4} - 24{x^3} + 57{x^2} + 18x - 45 = 0$, If one of them is $3 + i\sqrt 6 $, are
If $\alpha $, $\beta$, $\gamma$ are roots of ${x^3} - 2{x^2} + 3x - 2 = 0$ , then the value of$\left( {\frac{{\alpha \beta }}{{\alpha + \beta }} + \frac{{\alpha \gamma }}{{\alpha + \gamma }} + \frac{{\beta \gamma }}{{\beta + \gamma }}} \right)$ is
The number of solutions, of the equation $\mathrm{e}^{\sin x}-2 e^{-\sin x}=2$ is