Question

if x = to 2 upon 3 and x = 3 are roots of the quadratic equation ax²+ 7 x + b = 0 find the values of a and b

Answer 1

Answer is a=3 and b=6

Answer 2

Heya user
Here is your answer !!

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The two roots are ,
x = 3² = 9 ,
and ,
x = 3 .

So , putting the values in the quadratic equation , we get ,

f(x) = ax² + 7 x + b = 0
=> ( a * 9² ) + ( 7 * 9 ) + b = 0
=> 81a + 63 + b = 0
=> 81a + b = -63 . ----- ( 1 )

g(x) = ax² + 7 x + b = 0
=> ( a * 3² ) + ( 7 * 3 ) + b = 0
=> 9a + 21 + b = 0
=> 9a + b = -21 . ----- ( 2 )

So , solving ( 1 ) and ( 2 ) , we get ,

81a + b = -63
9a + b = -21. ( - )

=> 72a = - 42 .
=> a = - 42 / 72
=> a = - 7 / 12 . [ Answer ] .

and , putting the value in eq. ( 2 ) , we get ,

9a + b = -21
=> 9 * -7 / 12 + b = -21
=> -21 / 4 + b = -21
=> b = -21 + 21/4
=> b = ( -84 + 21 ) / 4
=> b = -63 /4 [ Answer ] .

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Hope it helps !!