*If *`x=2/3`* and x =−3 *are roots of the quadratic equation* ax ^{2} + 7x + b = 0,* find the values of a and b.

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#### Solution

The given equation is *ax*^{2} + 7*x* + *b* = 0.

Its roots are given as `x_1= −3` and `x_2=2/3`.

Now,

`=>x_1+x_2=-b/a`

`=>-3+2/3=(-(7))/a`

`=>(-9+2)/3=(-7)/a`

`=>(-7)/3=(-7)/a`

⇒ a = 3

Also

`=>x_1xxx_2=b/a`

`=>-3xx2/3=b/a`

`=>-2=b/3`

⇒ b = −6

Thus, the values of *a* and *b* are 3 and −6, respectively.

Concept: Nature of Roots

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