To find the x-intercepts of the quadratic equation given in the factored form \( y = (2x - 3)(x - 6) \), we need to set \( y \) equal to zero and solve for \( x \).
Setting the equation to zero:
\[ (2x - 3)(x - 6) = 0 \]
Now, we can set each factor equal to zero:
- \( 2x - 3 = 0 \)
- \( x - 6 = 0 \)
Solving the first equation:
\[ 2x - 3 = 0 \implies 2x = 3 \implies x = \frac{3}{2} \]
Solving the second equation:
\[ x - 6 = 0 \implies x = 6 \]
Thus, the x-intercepts of the quadratic equation are:
\[ x = \frac{3}{2} \quad \text{and} \quad x = 6 \]
Therefore, the x-intercepts are \(\left( \frac{3}{2}, 0 \right)\) and \((6, 0)\).
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