Sign of Quadratic Expressions

If $x^2+2ax+10-3a >0$ for all $x \in R$, then

If $b^2-4ac>0$ then the graph of $y=a{x}^2+bx+c$

If the equation $a{x}^2+2bx-3c=0$ has no real roots and $4\left(a+b\right)>3c$, then

The equation $\sin x=x^2+x+1$ has-

Find the real values of $x$ for which $(x^2-4x+1)$ is always negative.

The graph of quadratic polynomial $f\left(x\right)=(a-x)(x-b)$ where, $a, b>0$ and $a\ne b$, does not pass through

If $a\in \left(m,n\right)$, then the sign of $x^2-(a+2)x+4$ is always positive. Find the value of $-m+n$?

Find the least integral value of $k$ for which, $\left(k-2\right)x^2+8x+k+4>0$ for all $x\in R.$

If $x^2+2\mathrm{px}-2\mathrm{p}+8>0$ for all real values of $x$ then the set of all possible values of $p$ is

If $\alpha \in R^{-}$ and $\left(\alpha –2\right)x^2+8x+\alpha +4<0,\forall x\in R,$ then $\alpha$ cannot be ____

Find the largest integral value of $m$ for which the quadratic expression $y=x^2+\left(2m+4\right)x+7m+8$ is positive for all $x\in R$

For given figure of $y=f\left(x\right)=a{x}^2+bx+c$,

If graph of $f\left(x\right)=a{x}^2+bx+c$ is given by :

 The number of integral values of $k$ for which $x^2-2\left(4k-1\right)x+15k^2-2k-7\ge 0$ holds for all $x\in R$ is

The solution set of the equation $\left|x-1\right|+\left|4x-3x^2\right|=3x^2-3x-1$ is given by

Suppose a parabola $y=a{x}^2+bx+c$ has two $x$ intercepts, one positive and negative, and its vertex is $\left(2, -2\right)$ . Then which of the following is true?

Consider the figure of real quadratic $y=Q\left(x\right)=a{x}^2+bx+c$ as shown. Select the wrong option (Where $D=b^2-4ac, i=\sqrt{-1}$)

Let $f\left(x\right)$ be a quadratic expression which is positive for all $x$. If $g\left(x\right)=f\left(x\right)+f^{\text{'}}\left(x\right)+f^{\text{'}\text{'}}\left(x\right)$ then for all real $x$.

If $x^2+2ax+10-3a>0; x\in R$ then

If $b^2-4ac>0$ then the graph of $y=a{x}^2+bx+c$