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.
[tex]\begin{gathered} D=b^2-4ac \\ =(-7)^2-4\cdot(-4)\cdot3 \\ =49+48 \\ =97 \end{gathered}[/tex]
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.
[tex]\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} \\ =-\frac{7}{8}\pm\frac{\sqrt[]{97}}{-8} \\ =-\frac{7}{8}+\frac{\sqrt[]{97}}{8},-\frac{7}{8}-\frac{\sqrt[]{97}}{8} \end{gathered}[/tex]
So root of the equation are,
[tex]-\frac{7}{8}+\frac{\sqrt[]{97}}{8}\text{ and -}\frac{7}{8}-\frac{\sqrt[]{97}}{8}[/tex]
