Questions: c. Is the equation (3 x^2+5 x-2=4 x^2) linear or quadratic? Choose the correct answer below. quadratic linear d. Is the equation (6^2 x+5=0) linear or quadratic? Choose the correct answer below. quadratic linear

Solution Steps

a. To solve the linear equation $4x - 2 = 5$, we need to isolate $x$ by first adding 2 to both sides and then dividing by 4.

b. For the quadratic equation $2x^2 - 3 = -6$, we first add 6 to both sides to set the equation to zero, then solve for $x$ using the quadratic formula.

c. The equation $3x^2 + 5x - 2 = 4x^2$ is quadratic because it can be rearranged to the standard quadratic form $ax^2 + bx + c = 0$.

To solve the equation $4x - 2 = 5$, we first add 2 to both sides to get $4x = 7$. Then, we divide both sides by 4 to isolate $x$, resulting in $x = \frac{7}{4}$.

First, we add 6 to both sides to set the equation to zero: $2x^2 - 3 + 6 = 0$, which simplifies to $2x^2 + 3 = 0$. Solving for $x$, we find the solutions to be complex numbers: $x = \frac{\pm \sqrt{6}i}{2}$.

Rearrange the equation to the standard quadratic form: $3x^2 + 5x - 2 - 4x^2 = 0$, which simplifies to $-x^2 + 5x - 2 = 0$. Since the equation contains an $x^2$ term, it is a quadratic equation.

Final Answer