If \(2x^2 + kx - 14 = (x+2)(2x-7)\), find the value of K
Question 1 Report
If \(2x^2 + kx - 14 = (x+2)(2x-7)\), find the value of K
Answer Details
To find the value of k, we need to expand the right-hand side of the equation, which is equal to the left-hand side:
\begin{align*}
(x+2)(2x-7) &= 2x^2 - 3x - 14 \\
\end{align*}
Now we can compare the coefficients of the terms on both sides of the equation:
\begin{align*}
\text{Coefficient of } x^2: \quad &2 = 2 \\
\text{Coefficient of } x: \quad &-3 = k \\
\text{Coefficient of the constant term:} \quad &-14 = -14 \\
\end{align*}
Therefore, we have found that the value of k is -3.
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