If `(x+2) (x-5) =x^(2)+(a+b) x+a xx b` then value of (a+b) is

Options

A. 3
B. `-3`
C. 7
D. `-10`

Answer

To solve the equation \((x+2)(x-5) = x^2 + (a+b)x + ab\) and find the value of \(a+b\), we can follow these steps:

### Step 1: Expand the left-hand side
We start by expanding the expression \((x+2)(x-5)\).

\[ (x + 2)(x - 5) = x^2 - 5x + 2x - 10 \]

### Step 2: Combine like terms
Now, we combine the like terms from the expansion.

\[ x^2 - 5x + 2x - 10 = x^2 - 3x - 10 \]

### Step 3: Set the two sides equal
Now, we can set the expanded left-hand side equal to the right-hand side of the equation:

\[ x^2 - 3x - 10 = x^2 + (a + b)x + ab \]

### Step 4: Equate coefficients
Since the expressions are equal for all \(x\), we can equate the coefficients of \(x\) and the constant terms from both sides.

From the coefficients of \(x\):
\[ -3 = a + b \]

From the constant terms:
\[ -10 = ab \]

### Step 5: Solve for \(a + b\)
We already have the equation for \(a + b\):
\[ a + b = -3 \]

Thus, the value of \(a + b\) is \(-3\).

### Final Answer
The value of \(a + b\) is \(-3\).

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