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Question
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Solution
The given equation is ax2 + 7x + 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.
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