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The range of values of a so the all the roots of the equaton 2x^3-3x^2-12x+a=0 are real.

The range of values of a so the all the roots of the equaton
2x^3-3x^2-12x+a=0 are real.

Grade:9

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
8 years ago
Hello Student,

\\f(x)=2x^3-3x^2-12x+a \\f'(x)=6(x-2)(x+1) \\=>roots =2,-1 \\$now f(x) will have all roots real if $ \\f(-1)>0$ and $f(2)<0 \\=>-2-3+12+a>0$ and $16-12-24+a<0 \\=>-7<a<20
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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