If `alpha` , `beta` are the roots of the equation `x^2-4x-3 =0` , then `alpha^2+alpha*beta+ beta^2=` A. −13 B. 5 C. 13 D. 16 E. 19
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jeew-m
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`x^2-4x-3 = 0`
The roots of the above quadratic function is `alpha` and `beta` .
Then we know that;
`alpha+beta = -(-4)/1 = 4`
`alphaxxbeta = -3/1 = -3`
`alpha^2+alphaxxbeta+beta^2`
`= (alpha^2+beta^2)+alphaxxbeta`
`(x+y)^2 = x^2+2xy+y^2`
`(x^2+y^2) = (x+y)^2-2xy`
`alpha^2+alphaxxbeta+beta^2`
`= (alpha+beta)^2-2alphaxxbeta+alphaxxbeta`
`= 4^2-(-3)`
`= 19`
So the answer is 19 and it is at E)
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