Math, asked by sanjulvekush, 1 year ago

find the zeroes of polynomial f(x)=x³+5x²-16x+80,if its two zeroes are equal in magnitude but opposite in sign

Answers

Answered by hukam0685
12
let the zeros of polynomial
 \alpha  \:  \:  \:  ( - \alpha ) \:  \: and \ \:  \:  \: gamma  \\ sum \: of \: zeros \:  \alpha  -  \alpha  +  \gamma  =  \frac{ - b}{a}  =  - 5 \\  \gamma  =  - 5 \\ product \: of \: zeros \:   - { \alpha }^{2}  \gamma  = \frac{ - d}{a}  \\  =  - 80 \\  -  { \alpha }^{2} ( - 5) =  - 80 \\  { \alpha }^{2}  =  \frac{ - 80}{5}  =  - 1 6 \\  \alpha  =  \sqrt{ - 16}  \\  \alpha  =  +  - 4i \\ so \: zeros \: of \: polynomials \: are \:  - 5 \:  \:  \:  - 4i \:  \:  \:  \:  \:  + 4i
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