Question

Use the quadratic formula to find the roots of 4x^2-3=x^2-5x-4

Answer 1

Answer:

The roots are -0.232 and -1.435

Explanations:

The given equation is:

`4x^2-3=x^2-5x-4`

Simplify the equation by collecting like terms:

`\begin{gathered} 4x^2-x^2+5x-3+4=0 \\ 3x^2+5x+1=0 \end{gathered}`

a = 3, b = 5, c = 1

The quadratic formula is given as:

`\begin{gathered} x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}`

Substitute the values of a, b, and c into the formula above:

`\begin{gathered} x\text{ = }\frac{-5\pm\sqrt[]{5^2-4(3)(1)}}{2(3)} \\ x\text{ = }\frac{-5\pm\sqrt[]{25-12}}{6} \\ x\text{ = }\frac{-5\pm\sqrt[]{13}}{6} \\ x\text{ = }(-5\pm3.61)/(6) \\ x_1=\text{ }(-5-3.61)/(6) \\ x_1=\text{ }-1.435 \\ x_2=\text{ }(-5+3.61)/(6) \\ x_2=\text{ }(-1.39)/(6) \\ x_2=\text{ }-0.232 \end{gathered}`