If x=2/3 and x= -3 are the roots of the equation ax sauare + 7x + b = 0 find the value of a and b

If x=2/3 and x= -3 are the roots of the equation ax sauare + 7x + b =

1.	If x=2/3 and x= -3 are the roots of the equation ax sauare + 7x + b = 0 find the value of a and b
Answer» We have, ax2 + 7x + b = 0Since x = {tex}{2 \\over 3}{/tex}, -3 are the solutions of the given equationSubstitute x = {tex}{2 \\over 3}{/tex} in the given equation, we get{tex}a({2 \\over 3})^2 + 7({2 \\over 3})+b =0{/tex}{tex}\\implies {4a \\over 9} + {14 \\over 3} + b =0{/tex}Multiplying the equation by 9, we get4a + 9b + 42 = 0 ......(i)Now, substitute x = - 3 in the given equation, we geta(-3)2 + 7 (-3) + b = 09a +b - 21 = 0 ........(ii)Multiplying the equation by 9, we get81a +9b - 189 = 0 ........(ii)subtracting(ii) from (i), we get-77a = -231 or a = 3Substitue a =3 in (i), we get4(3) + 9b +42 = 0{tex}\\implies{/tex}9b + 54 = 0 or b = -6So, a = 3 and b = -6