Answer:

[tex]\boxed{\begin{aligned}& \qquad \:\sf \: a=5 \qquad \: \\ \\& \qquad \:\sf \: b= 3 \\ \\& \qquad \:\sf \: c= - 6\end{aligned}} \qquad \: \\ [/tex]

Step-by-step explanation:

Given quadratic polynomial is 5x² + 3x - 6

So, on comparing with general quadratic polynomial ax² + bx+ c, we get

[tex]\:\boxed{\begin{aligned}& \qquad \:\sf \: a=5 \qquad \: \\ \\& \qquad \:\sf \: b= 3 \\ \\& \qquad \:\sf \: c= - 6\end{aligned}} \qquad \: \\ [/tex]

Hence,

[tex]\implies \sf \:\boxed{\begin{aligned}& \qquad \:\sf \: a=5 \qquad \: \\ \\& \qquad \:\sf \: b= 3 \\ \\& \qquad \:\sf \: c= - 6\end{aligned}} \qquad \: \\ [/tex]

[tex]\rule{190pt}{2pt}[/tex]

Additional Information

[tex]\bf \:If\:\alpha, \beta \: are \: zeroes \: of \: {ax}^{2} + bx + c, \: then \\ [/tex]

[tex]\sf \: \alpha + \beta = - \dfrac{b}{a} \\ [/tex]

[tex]\sf \: \alpha \beta = \dfrac{c}{a} \\ [/tex]

[tex]\bf \:If\: \alpha, \beta, \gamma \: are \: zeroes \: of \: {px}^{3} + {qx}^{2} + rx + s, \: then\\ [/tex]

[tex]\sf \: \alpha + \beta + \gamma = - \dfrac{q}{p} \\ [/tex]

[tex]\sf \: \alpha \beta + \beta \gamma + \gamma \alpha = \dfrac{r}{p}\\ [/tex]

[tex]\sf \: \alpha \beta \gamma = - \dfrac{s}{p} \\ [/tex]