Question

If x=2/3 and x=-3 are the roots of the equation ax^2+7x+b=0 find the values of a and b

Answer 1

ANSWER:  

If x = $\frac{2}{3}$ and x = -3 are the roots of the equation, then values of a and b are 3, -6

SOLUTION:

Given, quadratic equation is $a x^{2}+7 x+b=0$ and its roots are -3 , $\frac{2}{3}$

We know that, for any quadratic equation of form $a x^{2}+b x+c=0$ with roots $x_{1} and x_{2}$ then,

Sum of roots $(x_{1} +x_{2})$ = $\frac{-b}{a}$

Product of roots ( $x_{1} \times x_{2})$ = $\frac{c}{a}$

Now, for given quadratic equation $x_{1}$ = -3 and $x_{2}$ = $\frac{2}{3}$

hence Sum of roots = $\frac{-7}{a}$

$x_{1} + x_{2} = \frac{-7}{a}$

$-3 + \frac{2}{3} = \frac{-7}{a}$

on solving we get "a" = 3

Now product of roots = $x_{1} \times x_{2} = \frac{b}{3}$

$-3 \times \frac{2}{3} = \frac{b}{3}$

b = -6

hence, the values of a and b are 3, -6.