Question

find Alpha square + beta square when quadratic equation is 44 x square - 4 x + 1​

Answer 1

f(x) = {x}^{2} - x - 4

Roots of the quadratic equation is alpha and beta.

Sum of the roots:

= > \: \alpha + \beta = \frac{ - b}{a}

= > \: \frac{ - ( - 1)}{1}

=> 1.

Product of zeroes:

= > \: \alpha \beta = \frac{c}{a}

=> -4/1

=> -4.

From the question,

= > \: \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta

= > \: \frac{ \alpha + \beta }{ \alpha \beta } - \alpha \beta

= > \: \frac{1}{ - 4} - ( - 4)

= > \: \frac{ - 1}{4} + 4

= > \: \frac{15}{4}