1.

If `alpha ` and `beta ` are the roots of the quadratic equation `x^(2) - 4x - 6 = 0 ` , find the values of `alpha^(2) + beta^(2)`.

Answer» Correct Answer - `alpha^(2) + beta^(2) = 28`
`x^(2) - 4x - 6 = 0 `
Here, `a= 1, b = - 4, c = - 6 `
`alpha + beta = ( - b)/( a) = ( - ( - 4))/( 1)= 4 ` ....(1)
`alpha beta = ( c )/( a ) = ( -6)/( 1) = - 6 ` ....(2)
`alpha^(2) + beta^(2) = ( alpha + beta)^(2) - 2alpha beta ` .....(identity )
`= ( 4)^(2) - 2( - 6)` ...[From (1) and (2) ]
` = 16 + 12 = 28`


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