Question

5. If a and B are the zeros of the quadratic polynomial f(x) = x2 - x - 4, find the value of
1/alpha +1/beta-alpha*beta​

Answer 1

Answer:

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Step-by-step explanation:

f(x) =  {x}^{2}  - x - 4 \\  \alpha  +  \beta  =  \frac{ - b}{a}  = 1   \\  \alpha  \beta  =  \frac{c}{a}  =  - 4 (1) \:  \:  \frac{1}{ \alpha }  +  \frac{1}{ \beta } =  \frac{ \alpha  +  \beta }{ \alpha  \beta }  -  \alpha  \beta   =  \frac{ - 1}{ 4}  - ( - 4)  \\  =  \frac{ - 1}{4}  + 4 \\  =  \frac{ - 1 + 16}{4}  \\  =  \frac{15}{4}