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x^(2)+9x+20
If
(x+a)(x+b) is equivalent to the given expression, what is the value of
a+b ?

$x^{2}+9 x+20$ $\newline$ If $(x+a)(x+b)$ is equivalent to the given expression, what is the value of $a+b$ ?

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Find trigonometric ratios using multiple identities

Full solution

Q.

x^{2}+9 x+20

\newline

If

(x+a)(x+b)

is equivalent to the given expression, what is the value of

a+b

?

Identify Numbers for Factoring: We need to factor the quadratic expression $x^2 + 9x + 20$ into the form $(x + a)(x + b)$ . To do this, we look for two numbers that multiply to $20$ (the constant term) and add up to $9$ (the coefficient of the $x$ term).
Calculate Numbers: The two numbers that satisfy these conditions are $4$ and $5$ , since $4 \times 5 = 20$ and $4 + 5 = 9$ .
Write Factored Form: Therefore, we can write the given expression as $(x + 4)(x + 5)$ .
Find Values of $a$ and $b$ : Now, we can find the values of $a$ and $b$ . From the factored form $(x + 4)(x + 5)$ , we can see that $a = 4$ and $b = 5$ .
Calculate $a + b$ : To find $a + b$ , we simply add the values of $a$ and $b$ together: $a + b = 4 + 5$ .
Calculate $a + b$ : To find $a + b$ , we simply add the values of $a$ and $b$ together: $a + b = 4 + 5$ .Calculating the sum gives us $a + b = 9$ .

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