Tag: some functions and their graphs -i

If $\alpha$ and $\beta$ are the polynomial  $f(x)=x^2-5x+k$ such that $\alpha-\beta=1$, then value of k is 

If $y^2 = ax^2 +bx+c$, then $y^2 \dfrac{d^2y}{dx^2}$ is

If $fxln\left(1+\dfrac{1}{x}\right)dx=p(x)ln\left(1+\dfrac{1}{x}\right)+\dfrac{1}{2}x-\dfrac{1}{2}ln(1+x)+c$, being arbitary costant, then

Let $f(x)$ is cubic polynomial with real coefficient such that $f''(3) = 0, f'(5) = 0$. If $f(3) = 1$ and $f(5) = -3$, then $f(1)$ is equal to

$f (x) = x^4 - 10x^3 + 35x^2 - 50x + c$ is a constant. the number of real roots of . f (x) = 0 and 
f'' (x) = 0 are respectively 

Let $\displaystyle f(x)=ax^{2}+bx+c,$ where $a,b,c$ are rational, and $f: Z\rightarrow Z,$ where $Z$ is the set of integers. Then $a+b$ is

The positive integers $x$ for which $f(x)=x^{3}-8x^{2}+20x-13$ is a prime is

If $f\quad \left( x \right) ={ x }^{ 2 }+2bx+{ 2c }^{ 2 }\quad and\quad g\quad (x)\quad ={ -x }^{ 2 }\quad -2cx+{ b }^{ 2 }\quad are\quad such\quad that\quad min\quad f\quad (x)\quad >\quad max\quad g\quad (x),\quad then$ relation between b and c, is

If $f(x)$ is a polynomial function satisfying $f(x)f\left(\dfrac{1}{x}\right)=f(x)+\left(\dfrac{1}{x}\right)$ and $f(3)=28$, then $f(4)=$

If $f\left(x\right)$ is a polynomial such that $ f\left(a\right) f\left(b\right)<0$, then number of zeros lieing between $a$ and $b$ is