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Question
If `x =2/3` and x = -3 are the roots of the quadratic equation `ax^2+2ax+5x ` then find the value of a and b.
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Solution
Given: `ax2 + 7x + b = 0`
Since, `x=2/3`is the root of the above quadratic equation
Hence, it will satisfy the above equation.
Therefore, we will get ,
`a(2/3)^2+7(2/3)+b=0`
⇒ `4/9a+14/3+b=0`
⇒ `4a+42+9b=0`
⇒ `4a+9b=-42` .............(1)
Since, x = –3 is the root of the above quadratic equation
Hence, It will satisfy the above equation.
Therefore, we will get
`a(-3)^2+7(-3)+b=0`
`⇒ 9a-21+b=0`
`⇒9a+b=21` ......................(2)
From (1) and (2), we get
a = 3, b = –6
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