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Home » \[ x^2 = 25 \] - DevRocket

\[ x^2 = 25 \] - DevRocket

📅 May 3, 2026 👤 scraface

May 03, 2026

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#### 19.47
The function \( f(x) = ax^2 + bx + c \) has roots at \( x = 2 \) and \...
The function can be expressed in factored form based on the roots:
f(x) = a(x - 2)(x + 3)
Expand the expression:
f(x) = a(x^2 + 3x - 2x - 6) = a(x^2 + x - 6)
Substitute \( x = 1 \) into the expanded form and set it equal to 6:
f(1) = a(1^2 + 1 - 6) = 6
a(-4) = 6
a = \frac{6}{-4} = -\frac{3}{2}

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