Question

Question:-

Answer 1

Step-by-step explanation:

If x = 2/3, x = -3 are roots, then the eqn will be

→

(x-

2

3

)

{x-(-3)}=0

→

(x-

2

3

)

{(x+3)} = 0

→

x

2

-

2

3

x + 3x - 2= 0

⇒ 3

x

2

-2x+9x-6=0

⇒ 3

x

2

+7x-6=0 is the required eqn.

Compare the eqn with ax²+7x+b=0

We have a=3, b=7 c= -6

hope it's help you ....

Answer 2

Answer:

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

given - an equation and its roots !

To find - values of a and b in the given equation ~

$Quadratic \: eq {}^{n} = ax {}^{2} + 7x + b = 0$

roots of the question are $\dashrightarrow - 3 \: and \: \frac{2}{3}$

Now ,

$Sum \: of \: zeroes \: ( \: \alpha \: + \: \beta \: ) = - \frac{ - b}{a} \\ \\ \implies \: - 3 + \frac{2}{3} = \frac{ - 7}{a} \\ \\ \implies \: \frac{ - 9 + 2}{3} \\ \\ \implies \frac{ - 7}{3} = \frac{ - 7}{a} \\ \\ \underline{on \: comparing} \\ \\\bold\red{\implies \:a = 3}$

further ,

$Product \: of \: zeroes \: ( \: \alpha \: \times \beta \: ) = \frac{c}{a} \\ \\ \implies \: (- \cancel {3})( \frac{2}{\cancel3} ) = \frac{b}{a} \\ \\ \implies \: - 2 = \frac{b}{3} \\ \\ \implies \: b = 3 \times - 2 \\ \\ \bold\red{\implies \: b = - 6}$

hope helpful :D