If x=2/3 and x= -3 are roots of the equation ax 2 + 7x +b=0, find the values of a and b.
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2/3,-3 are the roots of the equation ax²+7x+b=0
then from the relation between roots and coefficients, sum fo the roots=-7/a
or, -7/a=2/3+(-3)=2/3-3
or, -7/a=-7/3
or, 1/a=1/3
or, a=3 and
product of the roots=b/a
or, b/a=2/3×(-3)
or, b=a×(-2)
or, b=3×(-2)
or, b=-6
then from the relation between roots and coefficients, sum fo the roots=-7/a
or, -7/a=2/3+(-3)=2/3-3
or, -7/a=-7/3
or, 1/a=1/3
or, a=3 and
product of the roots=b/a
or, b/a=2/3×(-3)
or, b=a×(-2)
or, b=3×(-2)
or, b=-6
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