1.

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

Answer»

all real roots
all IMAGINARY roots
EXACTLY two real and two imaginary roots
none

Solution :`(c )` `f(x)=ax^(4)+bx^(3)+cx^(2)+5x-7`
`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.


Discussion

No Comment Found

Related InterviewSolutions