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

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.

Concept: Nature of Roots
Is there an error in this question or solution?