Answer:
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
given - an equation and its roots !
To find - values of a and b in the given equation ~
[tex]Quadratic \: eq {}^{n} = ax {}^{2} + 7x + b = 0 \\ [/tex]
roots of the question are [tex] \dashrightarrow - 3 \: and \: \frac{2}{3} \\ [/tex]
Now ,
[tex]Sum \: of \: zeroes \: ( \: \alpha \: + \: \beta \: ) = - \frac{ - b}{a} \\ \\ \implies \: - 3 + \frac{2}{3} = \frac{ - 7}{a} \\ \\ \implies \: \frac{ - 9 + 2}{3} \\ \\ \implies \frac{ - 7}{3} = \frac{ - 7}{a} \\ \\ \underline{on \: comparing} \\ \\\bold\red{\implies \:a = 3}[/tex]
further ,
[tex]Product \: of \: zeroes \: ( \: \alpha \: \times \beta \: ) = \frac{c}{a} \\ \\ \implies \: (- \cancel {3})( \frac{2}{\cancel3} ) = \frac{b}{a} \\ \\ \implies \: - 2 = \frac{b}{3} \\ \\ \implies \: b = 3 \times - 2 \\ \\ \bold\red{\implies \: b = - 6}[/tex]
hope helpful :D
