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Maths-

General

Easy

Question

$5 left parenthesis x plus a right parenthesis plus 3 open parentheses x squared minus a close parentheses equals 3 x squared plus 5 x plus 2$
In the equation above, a is a constant. If the equation is true for all values of x, what is the value of a?

The correct answer is: 1

Hint:
The concept used in the question is concept of the equation.
Given equations are linear equations in two variables.
In the elimination method, any of the coefficients is first equated and eliminated. After elimination, the equations are solved to obtain the other equation.
Step by step explanation:
Given:
5(x + a) + 3(x² − a) = 3x² + 5x + 2
Step 1:
Simplify the right side:
5(x + a) + 3(x² − a)
⇒ 5x + 5a + 3x² - 3a
⇒ 3x²+ 5x + 5a - 3a
⇒ 3x²+ 5x + 2a
Step 2:
Compare the both side
As LHS = RHS
3x²+ 5x + 2a = 3x² + 5x + 2
∴ 2a = 2
⇒ a = $2 over 2$
⇒ a = 1
∴ a = 1

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