Answer:
1. Quadratic; [tex]3x^2 + 11x+10=0[/tex]
2. Not quadratic
3. Not quadratic
4. Not quadratic
5. Quadratic; [tex]3x^2-14x-7=0[/tex]
Step-by-step explanation:
A quadratic equation is a polynomial whose highest degree is two and does not include any terms that are to a negative or non-integer power. For example, [tex]f(x) = x^2 + 5x -3[/tex] or [tex]f(x) = (x+4)^2[/tex]. To determine if the following equations are quadratic, look at the powers of the terms.
The standard form of a quadratic equation is [tex]ax^2+bx+c=0[/tex].
1. [tex]3x^2 + 11x+10=0[/tex] is a quadratic equation. It is already in standard form, so no rearranging is necessary.
2. [tex]x + \frac{1}{x} =4[/tex] is not a quadratic equation because the highest degree is 1.
3. [tex]x - \frac{5}{x} =x^2[/tex] is not a quadratic equation. Even though the highest degree is two, this is a rational equation (has a variable in the denominator of a fraction). So, the graph is not a parabola and this is not a quadratic equation.
4. [tex]x^2-\sqrt{5x} +7=0[/tex] is also not a quadratic equation. 5x is to the power of 1/2, which is a non-integer exponent. Therefore, this is not considered a quadratic equation.
5. [tex](2x-1)^2-(x+3)^2=4x[/tex] is a quadratic equation. To rewrite it into standard form, distribute the squares and bring all terms to one side.
[tex](4x^2-4x+2)-(x^2+6x+9)=4x\\3x^2-14x-7=0[/tex]