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If a, b. c in R and 3b^(2)-8ac lt 0, then the equation ax^(4)+bx^(3)+cx^(2)+5x-7=0 has |
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Answer» all real roots `f'(x)=4ax^(3)+3BX^(2)+2cx+5` `f''(x)=12ax^(2)+6bx+2c=0` `implies "disc"=36b^(2)-4(12a)(2c)` `=12(3b^(2)-8ac) lt 0` `(:' 3b^(2) lt 8ac)` `f'(x)=0` has only one real root `implies f(x)=0` has exactly two real roots. |
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