Question
2 If \( 2 x^{2}-5 x+\mathrm{a}=(2 x-3)(x-1) \), then \( \mathrm{a}=\cdots \cdots \ldots \ldots \ldots \ldots \) (a) 2
Ask by Reeves Barker. in Egypt
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( a = 3 \)
Solution
Expand the right-hand side of the equation:
\[
(2x-3)(x-1) = 2x \cdot x - 2x \cdot 1 - 3 \cdot x + 3 \cdot 1 = 2x^2 - 2x - 3x + 3 = 2x^2 - 5x + 3.
\]
Since both sides of the equation must be identical for all \( x \), we equate the constant terms on both sides:
\[
a = 3.
\]
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Simplify this solution Bonus Knowledge
To find the value of \( a \), we first need to expand the right side of the equation \( (2x - 3)(x - 1) \). Expanding it gives: \[ (2x - 3)(x - 1) = 2x^2 - 2x - 3x + 3 = 2x^2 - 5x + 3. \] Now we have: \[ 2x^2 - 5x + a = 2x^2 - 5x + 3. \] For the equations to be equal, the constants must also be equal, which means: \[ a = 3. \] So, \( a = 3 \).
