Step 1:
Write the function
[tex]f(x)=-2x^2\text{ + 4ax + 3}[/tex]
Step 2:
From a quadratic formula
A negative discriminant indicates that neither of the solutions are real numbers.
[tex]\begin{gathered} \text{Discriminant D = b}^2\text{ - 4ac} \\ \end{gathered}[/tex]
Step 3
for non real values , D < 0
[tex]b^2\text{ - 4ac < 0}[/tex]
Step 4:
From the general equation of the quadratic equation
[tex]\begin{gathered} ax^2\text{ + bx + c = 0} \\ a\text{ = -2} \\ b\text{ = 4a} \\ c\text{ = 3} \end{gathered}[/tex]
Step 5:
[tex]\begin{gathered} b^2\text{ - 4ac < 0} \\ (4a)^2\text{ - 4(-2)(3) < 0} \\ 16a^2\text{ + 24 < 0} \\ 16a^2\text{ < -}24 \\ a^2\text{ < }\frac{-24}{16} \\ a^2\text{ < }\frac{-3}{2} \\ a\text{ <}\pm\text{ }\sqrt[]{\frac{-3}{2}} \\ a\text{ < i}\sqrt[]{\frac{3}{2}\text{ }}\text{ or a < -}\sqrt[]{\frac{3}{2}} \end{gathered}[/tex]
Final answer
False
