To solve the given equation [tex]\( ax^2 + bx + c \)[/tex] under the condition that [tex]\( a = 0 \)[/tex], let's carefully analyze the situation step-by-step:
1. Original Equation:
The original quadratic equation given is:
[tex]\[
ax^2 + bx + c
\][/tex]
2. Substitute [tex]\( a = 0 \)[/tex] into the Equation:
We know that [tex]\( a = 0 \)[/tex]. Substituting this value into the equation, we get:
[tex]\[
0 \cdot x^2 + bx + c
\][/tex]
3. Simplify the Equation:
Since the term [tex]\( 0 \cdot x^2 \)[/tex] effectively becomes zero, it disappears from the equation. Thus, the equation simplifies to:
[tex]\[
bx + c
\][/tex]
4. Conclusion:
When [tex]\( a = 0 \)[/tex], the quadratic equation [tex]\( ax^2 + bx + c \)[/tex] is reduced to the linear equation:
[tex]\[
bx + c
\][/tex]
Hence, the equation [tex]\( ax^2 + bx + c \)[/tex] simplifies to [tex]\( bx + c \)[/tex] when [tex]\( a = 0 \)[/tex].
