Q10.

Q:::) (x-1)(x-2)(x-3)(x-4)=15
find no.of +ive solutions..
A:) simplyfy to get x4-10x3+35x2-50x+9=0 ---a
+ - + - + : 4 sign changes imply 4 real roots exist.
differentiate to get 4x3-30x2+70x-50=0 ----b
differentiate to get 12x2-60x+70=0 -----c
both roots of 'c' are positive...(obvious)..and f(0)>0
hence dy/dx =0 for 'b' at points say 'p','q' where both>0
and fb(0)<0> all 3 roots of (B) are positive... since for (b) f(inf)=inf & f(-inf)=-inf
coming bak to (a)...dy/dx=0 at 3 points ....and all are positive....further f(0)>0 and f(inf)=f(-inf)=inf.....hence all roots are positive...

thus answer should be 4 but no such option exixts..