`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...*

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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)*

**Further Reading**