Question 1 - Long division — finding remainder; minimum of quadratic; line through two points; turning points Practice | Prasnya
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Long division —...
Question 1
00:00
Est. 4 min
Marks:
+4.00
0.00
Consider two polynomials
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
p(x) = x^4 + 3x^3 - 9x + 8
and
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
q(x) = (x^2 + x)(x + 3)
. Let
r
(
x
)
r(x)
be the remainder obtained when
p
(
x
)
p(x)
is divided by
q
(
x
)
q(x)
. Let
l
(
x
)
l(x)
be the straight line passing through the
y
y
-intercept and the minimum point of
r
(
x
)
r(x)
. Which of the following options is/are true?
Multiple correct
Hard Difficulty
23 February 2025
A
r
(
x
)
=
−
16
x
2
+
4
x
−
8
r(x) = -16x^2 + 4x - 8
B
l
(
x
)
=
y
=
−
3
x
+
8
l(x) = y = -3x + 8
C
l
(
x
)
=
y
=
−
2
x
+
8
l(x) = y = -2x + 8
D
p
(
x
)
p(x)
has at most 4 turning points.
