$$ 2 x^{2}+p x+6=(2 x-a)(x-2) $$ इकणि अट्डा शवन, $$ a $$ © $$ p $$ -

Question

UpStudy AI · Accepted Answer

**Step 1. Expand the right-hand side**

The given equation is  
$$
2 x^{2}+p x+6=(2 x-a)(x-2).
$$

Expanding the right-hand side, we get:
$$
\begin{aligned}
(2x-a)(x-2) &= 2x(x-2) - a(x-2) \
            &= 2x^2 - 4x - ax + 2a \
            &= 2x^2 - (a+4)x + 2a.
\end{aligned}
$$

**Step 2. Equate coefficients**

Since the equation holds for all values of $$ x $$, the coefficients of corresponding powers of $$ x $$ must be equal. That is:
$$
2x^2 + px + 6 = 2x^2 - (a+4)x + 2a.
$$

This gives us two equations by comparing coefficients:

- Coefficient of $$ x $$:
  $$
  p = -(a+4).
  $$
- Constant term:
  $$
  6 = 2a.
  $$

**Step 3. Solve for $$ a $$ and $$ p $$**

From the constant term:
$$
6 = 2a \implies a = 3.
$$

Now, substitute $$ a = 3 $$ into the equation for $$ p $$:
$$
p = -(3+4) = -7.
$$

**Final Answer**

$$
a = 3,\quad p = -7.
$$
$$ a = 3 $$ and $$ p = -7 $$.

\( 2 x^{2}+p x+6=(2 x-a)(x-2) \) इकणि अट्डा शवन, \( a \) © \( p \) -

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