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Quadratic Equation

Determine with explanation wether each equation is quadratic or not.

1. x = 5 - 33x

2. x + 1.5x² + 9x⁴ = 0

3. 8x + 2 + 5x² = 4

4. 4x² + 13x - 4x² = 3

5. 8x³ + 6 = 3 - 4x²

6. (9 + x) (x + 2) = 3x​

Sagot :

Analyze equation 1, x=5-3x. This is not a quadratic equation because it does not contain a term with
x
2
x
2

2 Analyze equation 2,
x
+
1.5
x
2
+
9
x
4
=
0
x+1.5x
2
+9x
4
=0. This is not a quadratic equation because it contains a term with
x
4
x
4
, which is not allowed in a quadratic equation
3 Analyze equation 3,
8
x
+
2
+
5
x
2
=
4
8x+2+5x
2
=4. Rearrange the equation to get
5
x
2
+
8
x
−
2
=
0
5x
2
+8x−2=0. This is a quadratic equation because it is in the form
a
x
2
+
b
x
+
c
=
0
ax
2
+bx+c=0
4 Analyze equation 4,
4
x
2
+
13
x
−
4
x
2
=
3
4x
2
+13x−4x
2
=3. Simplify the equation to get 13x-3=0. This is not a quadratic equation because it does not contain a term with
x
2
x
2

5 Analyze equation 5,
8
x
3
+
6
=
3
−
4
x
2
8x
3
+6=3−4x
2
. Rearrange the equation to get
8
x
3
+
4
x
2
+
3
=
0
8x
3
+4x
2
+3=0. This is not a quadratic equation because it is a cubic equation, not a quadratic equation.
Therefore, the equations are:
1​. Not quadratic
2​. Not quadratic
3​. Quadratic
4​. Not quadratic
5​. Not quadratic
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