Respuesta :
[tex]-4 x^{2}+5 x-4=0[/tex] will not have real roots that means quadratic equation do not have real solution.
Solution:
Need to determine the real solutions for following quadratic equations
[tex]-4 x^{2}+5 x-4=0[/tex]
First let’s check whether the given quadratic equation have real roots or not
[tex]\begin{array}{l}{\text { General quadratic equation } a x^{2}+b x+c=0 \text { will have real roots only }} \\ {\text { when } b^{2}-4 a c>0}\end{array}[/tex]
In our case, equation is [tex]-4 x^{2}+5 x-4=0[/tex]
Here a = -4, b = 5 and c = -4
Substituting the values in [tex]b^{2}-4 a c[/tex]
[tex]\begin{array}{l}{\Rightarrow \mathrm{b}^{2}-4 \mathrm{ac}=5^{2}-4 \times(-4) \times(-4) } \\\\ {=25-64=-39}\end{array}[/tex]
So since in our case [tex]\mathrm{b}^{2}-4 \mathrm{ac}=-39[/tex] which is not greater than zero, so quadratic equation [tex]-4 x^{2}+5 x-4=0[/tex] will not have real roots that means quadratic equation do not have real solution.
