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CBSE
MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials
Problem
Let
f
(
x
)
=
3
x
3
+
4
x
2
+
13
x
+
4
f(x)=3x^3+4x^2+13x+4
f
(
x
)
=
3
x
3
+
4
x
2
+
13
x
+
4
. (1) Show that
(
3
x
+
1
)
(3x+1)
(
3
x
+
1
)
is a factor of
f
(
x
)
f(x)
f
(
x
)
. (2) Factorise
f
(
x
)
f(x)
f
(
x
)
completely. (3) Prove that there are no real solutions to
3
sec
2
θ
+
4
sec
θ
+
13
+
4
cos
θ
=
0
3\sec^2\theta+4\sec\theta+13+4\cos\theta=0
3
sec
2
θ
+
4
sec
θ
+
13
+
4
cos
θ
=
0
.
Related theory
Nature of Roots
Quadratic Equations
Factorisation of Polynomials
Polynomials
Functions
Solving quadratic equations
Algebra
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