Question

$\frac{4a}{9}$+b=$\frac{-14}{3}$
9a+b=21

find values of a and b

Answer 1

Step-by-step explanation:

Hm… First use the roots to write the polynomial in factored form:

ax2+7x+b=0 , where x′=23 and x′′=−3

a(x−23)(x+3)=0

See why this is true? Then distribute the whole thing:

(ax+3a)(x−23)=0

ax2+(3−23)ax−2a=0

ax2+(7a3)x−2a=0

Here we get that

−2a=b

And

7a3=7

Solving that we have

a=737=3

And

b=−2(3)=−6

Voilá! Er… I mean… QED