if x =2/3 and x=-3are the roots of the quadratic equation ax² +7x+b=0then find value of a and b
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P(2/3)=a(2/3)^2+7(2/3)+b
=4/9a+b+14/3 eq1
P(-3)= a(-3)^2+7(-3)+b
= 9a-21+b. Eq2
on subtracting eq1 from 2
9a -4/9×a -21-14/3 +b-b =0
77/9×a-77/3=0
77/9×a=77/3
a=3
Then from eq(2)
9(3)-21+b=0
27-21+b=0
6+b=0
b=-6
=4/9a+b+14/3 eq1
P(-3)= a(-3)^2+7(-3)+b
= 9a-21+b. Eq2
on subtracting eq1 from 2
9a -4/9×a -21-14/3 +b-b =0
77/9×a-77/3=0
77/9×a=77/3
a=3
Then from eq(2)
9(3)-21+b=0
27-21+b=0
6+b=0
b=-6
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