Question

if X=-3 and X=2/3 are solutions of quadratic equation mx^2+7x+n=0, find the values of m and n
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Answer 1

quadratic eq=p(x)=mx²+7x+n=0,

zeros of p(x) are

x=-3 and x=2/3,

case 1: putting x=-3 in p(x)

m(-3)²+7(-3)+n=0,

9m-21+n=0,

9m+n=21---(1)

case 2: putting x=2/3,

m(2/3)²+7(2/3)+n=0,

4m/9+14/3+n=0,

4m+42+9n=0,

4m+9n=-42---(2),

multiplying (1) by 9 both side,

81m+9n=189---(3),

sub eq2 from 3,

81m-4m+9n-9n=189-(-42),

77m=231,

m=231/77=3,

by putting m=3 in 1 we get,

9(3)+n=21,

n=21-27=-6