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If x=2/3 and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b. - CBSE Class 10 - Mathematics

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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`

⇒ 3

Also

`=>x_1xxx_2=b/a`

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

`=>-2=b/3`

⇒ 6

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

  Is there an error in this question or solution?
Solution If x=2/3 and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b. Concept: Nature of Roots.
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