Geometrical Meaning of the Zeroes of a Polynomial

The graph of a polynomial $p\left(x\right)= a{x}^2+bx+c$ is given as:

If $\alpha \text{and} \beta$ are its zeroes, then find the value of $\alpha \text{and} \beta$

Draw the graph of the quadratic polynomial $f\left(x\right)=x^2-4x+3$ and observe:

 It's number of zeros

Draw the graph of the quadratic polynomial $f\left(x\right)=x^2-4x+3$ and observe:

$$The shape of the curve when the coefficient of $x^2$ is negative,

Draw the graph of the quadratic polynomial $f\left(x\right)=x^2-4x+3$ and observe:

The shape of the curve when the coefficient of $x^2$ is positive,

Draw the graph of $3x^2-x-4$ and find the zeroes.

Draw the graph of following polynomial:

$-4x^2+4x-1$.

Draw the graph of $x^2+x-12=0$ and state the nature of their solution.

Draw the graph of $p\left(x\right)=x^2+5x+6$

Draw the graph of the polynomial $f\left(x\right)=2x^2-4x+5$.

If the graph of a quadratic polynomial lies entirely below $x$-axis, then both the roots are not real.

Identify the graph of a fourth degree polynomial

If the graph of a quadratic polynomial lies entirely below $x$-axis, then 

In the above figure, the graph of a polynomial p(x) is shown. The number of zeroes of p(x) is:

If the graph of a polynomial intersects the $x-\mathrm{axis}$ at only one point, it cannot be a quadratic polynomial.

If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial

The graph of the quadratic polynomial $a{x}^2+bx+c$ intersect x-axis such that $c=\frac{b^2}{4a}$, then the quadratic polynomial has

If $a > 0$, then the graph of the quadratic polynomial will be an _____opening parabola.

The point where the graph of the equation $x^2–2x–8=0$ intersects $X-$axis are $(x,0) \mathrm{and} (–2,0)$, then the value of $x$ ?

If $p\left(x\right) = 4x + 5$, then the root of $p\left(x\right)$ is