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

sub x=2/3 in ax^2 +7x+b=0
a(2/3)^2 +7(2/3)+b=0
4a/9+14/3 +b=0
4a+42+9b=0
4a+9b=-42
substitute x=-3
a(9)+7(-3)+b=0
9a+b=21
solve them
4a+9b=-42
9a+b=21
4a+9b=-42
81a+9b=189
-77a=-231
a=231/77
a=21/7
a=3
sub in 9a +b=21
9(3)+b=21
27+b=21
b=21-27
b=-6
a=3,b=-6 is answer