MathDB
Problems
Contests
National and Regional Contests
India Contests
India LIMIT
2020 LIMIT
2020 LIMIT Category 2
3
3
Part of
2020 LIMIT Category 2
Problems
(1)
No real roots, quadratic in disguise
Source: LIMIT 2020 Cat 2 Obj P3
5/25/2020
Given that the equation
(
m
2
−
12
)
x
4
−
8
x
2
−
4
=
0
(m^2-12)x^4-8x^2-4=0
(
m
2
−
12
)
x
4
−
8
x
2
−
4
=
0
has no real roots, then the largest value of
m
m
m
is
p
q
p\sqrt{q}
p
q
, where
p
p
p
and
q
q
q
are natural numbers,
q
q
q
is square-free. Determine
p
+
q
p+q
p
+
q
.(A)
4
4
4
(B)
5
5
5
(C)
3
3
3
(D)
6
6
6
limit
algebra