Question

Quadratic Formula Problem: - 4x - 7x + 3 = 0Read directions, in picture attached, please

Answer 1

For the quadratic equation -4x^2 - 7x + 3 = 0, the value oc coefficients are,

a = -4, b = -7 and c = 3.

Determine the value of determinant for the quadratic equation.

`\begin{gathered} D=b^2-4ac \\ =(-7)^2-4\cdot(-4)\cdot3 \\ =49+48 \\ =97 \end{gathered}`

The value of determinant is greater than 0, so quadratic equation has two different real roots.

Determine the roots of the equation by using quadratic formula.

`\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4\cdot(-4)\cdot3}}{2\cdot(-4)} \\ =\frac{7\pm\sqrt[]{49+48}}{-8} \\ =\frac{7\pm\sqrt[]{97}}{-8} \\ =-(7)/(8)\pm\frac{\sqrt[]{97}}{-8} \\ =-(7)/(8)+\frac{\sqrt[]{97}}{8},-(7)/(8)-\frac{\sqrt[]{97}}{8} \end{gathered}`

So root of the equation are,

`-(7)/(8)+\frac{\sqrt[]{97}}{8}\text{ and -}(7)/(8)-\frac{\sqrt[]{97}}{8}`