+26367 Find 
if the expansion of the product of 
and 
has no 
term.
$$\small{\text{
$
(x^3 - 4x^2 + 2x - 5)*( x^2 + tx - 7) = tx^4-4tx^3+\textcolor[rgb]{1,0,0}{2tx^2}-5tx+x^5-4x^4-5x^3+\textcolor[rgb]{1,0,0}{23x^2}-14x+35
$
}}$$
$$\\ \small{\text{
Set $
\textcolor[rgb]{1,0,0}{2tx^2}+\textcolor[rgb]{1,0,0}{23x^2} = 0
$
than the product has no $x^2$, t must be a constant!
}}
\\\\
2tx^2 + 23x^2 = 0 \\\\
2tx^2 = - 23x^2 \quad | \quad : 2x^2 \\\\
t= -\frac{23}{2} = - 11.5$$
$$\small{\text{
$
\textcolor[rgb]{1,0,0}{t= -11.5}\qquad (x^3-4x^2+2x-5)*(x^2+\textcolor[rgb]{1,0,0}{(-11.5)}x-7) = x^5 - 15.5x^4+41x^3+43.5x+35
$
}}$$
There is no more $$x^2$$
+26367 Find if the expansion of the product of and has no term.
$$\small{\text{
$
(x^3 - 4x^2 + 2x - 5)*( x^2 + tx - 7) = tx^4-4tx^3+\textcolor[rgb]{1,0,0}{2tx^2}-5tx+x^5-4x^4-5x^3+\textcolor[rgb]{1,0,0}{23x^2}-14x+35
$
}}$$
$$\\ \small{\text{
Set $
\textcolor[rgb]{1,0,0}{2tx^2}+\textcolor[rgb]{1,0,0}{23x^2} = 0
$
than the product has no $x^2$, t must be a constant!
}}
\\\\
2tx^2 + 23x^2 = 0 \\\\
2tx^2 = - 23x^2 \quad | \quad : 2x^2 \\\\
t= -\frac{23}{2} = - 11.5$$
$$\small{\text{
$
\textcolor[rgb]{1,0,0}{t= -11.5}\qquad (x^3-4x^2+2x-5)*(x^2+\textcolor[rgb]{1,0,0}{(-11.5)}x-7) = x^5 - 15.5x^4+41x^3+43.5x+35
$
}}$$
There is no more $$x^2$$
