The graph of the polynomial f(x) = ax2 + bx + c is as shown below


The graph of the polynomial $f(x)=a x^{2}+b x+c$ is as shown below (Fig. 2.19). Write the signs of 'a' and $b^{2}-4 a c$.



Clearly, $f(x)=a x^{2}+b x+c$ represent a parabola opening upwards. Therefore, $a>0$

Since the parabola cuts x-axis at two points, this means that the polynomial will have two real solutions

Hence $b^{2}-4 a c>0$

Hence $a>0$ and $b^{2}-4 a c>0$

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