x=2÷3 and x= -3 are roots of quadratic equation ax²+7x+b=0 find the vaues of a and b
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given roots ,
x = 2 / 3 , x = - 3
given equation,
ax^2 + 7x + b = 0 ---eq.(1)
put, x = 2 / 3 in (1)
a ( 2/ 3 )^2 + 7 (2/3) + b = 0
4a / 9 + b = - 14 / 3 ---------------eq.( 2 )
put x = - 3 in (1)
a(-3 )^2 + 7(-3) + b =0
9a +b = 21 ---------(3)
subtract eq.(2) from eq. (3)
9a - 4a / 9 = 21 + 14 / 3
77a / 9 = 77 / 3
a =77 ×9 / 3×77
a = 9 / 3 = 3
a = 3
put value of a in eq. (3) ,we get,
b = 21 - 27
b = - 6
hence, a = 3 and b = - 6
◆hope it helps ◆
x = 2 / 3 , x = - 3
given equation,
ax^2 + 7x + b = 0 ---eq.(1)
put, x = 2 / 3 in (1)
a ( 2/ 3 )^2 + 7 (2/3) + b = 0
4a / 9 + b = - 14 / 3 ---------------eq.( 2 )
put x = - 3 in (1)
a(-3 )^2 + 7(-3) + b =0
9a +b = 21 ---------(3)
subtract eq.(2) from eq. (3)
9a - 4a / 9 = 21 + 14 / 3
77a / 9 = 77 / 3
a =77 ×9 / 3×77
a = 9 / 3 = 3
a = 3
put value of a in eq. (3) ,we get,
b = 21 - 27
b = - 6
hence, a = 3 and b = - 6
◆hope it helps ◆
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