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Fill in the blanks If the quadratic equations `x^2+a x+b=0a n dx^2+b x+a=0(a!=b)` have a common root, then the numerical value of `a+b` is ________.

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Let ` alpha ` be a common root between given quadratic equations.
Then ` alpha^(2) + aalpha + b=0`
`alpha^(2) + balpha + a=0`
On subtration.
`( a-b) alpha + b -a = 0 Rightarrow alpha =1`
The common root is 1. putting ,` alpha =1 `, we get
` 1 + a+ b =0 Rightarrow a + b = -1 Rightarrow |a +b| =1`
` Rightarrow ` Absolute value of (a +b) =1
Numerical value of a +b is -1.
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