1ur prove is only for integral roots [3][3][3][4][4][4][9][4]
prove again when d/a is fraction
1) Let a,b,c,d be 4 integers such that ad is odd, & bc is even.
Then, ax3+ bx2+ cx +d=0 has-
A) At least 1 Irrational root.
B) All 3 Irrational roots.
C) All 3 Integral roots.
D) None of these.
2) Let f(x)= ax2 +bx +c, a,b,c ε R.
If f(x) takes real values for real values of x, & non-real values for non-real values of x, then-
A) a=0 B) b=0
C) c=0 D) Nothing can be said about a,b,c.
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17 Answers
1how cn u say (d/a) is odd?? it may b a fraction...like suppose a is 3 and d is 5....ad is 15 which is odd...but d/a is 5/3...
1
1lolzzzzzzzz dude harsh.....i've proved that one of them is imaginary ....
1solve for
a=d
b=c
from here u find x=-1 as one root and it will show that other roots can be imaginary
11)
according to given question
the equation can also be
x^{3}+2x^{2}+2x+1=0
it has one integral root and two imaginary roots
so most suitable answer is d
1arrey oo bhai abhirup.....!!!
it's for the worst case dat i've considered....try doing it without this logic....if you can ...call me up !!! :-)
11(A)
Let roots be α, β, γ which are rational.
as ad is odd so a= odd ; d= odd
so αβγ = -(d/a) = odd
so α, β, γ are all odd.
now α+β+γ = odd = -(b/a) so , b is odd.
So sigma αβ = odd =(c/a) so, c is odd.
but bc = even (given)
and bc according to our soln. is odd x odd = odd no.
So the question is where we have gone wrong.
It's so due to our assumption that all roots are rational.
So ans. : (A)
Please verify.