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Home » ≈ 1.2089 × 10¹⁹ — but for math competition, better to compute difference: - Abu Waleed Tea

≈ 1.2089 × 10¹⁹ — but for math competition, better to compute difference: - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A quadratic function \( f(x) = ax^2 + bx + c \) has roots at \( x = 2 \) and \( x = -3 \). If \( f(1) = 6 \), find the value of \( a \).

📌 Since the roots are 2 and -3, the function can be written as \( f(x) = a(x - 2)(x + 3) \).

📌 Expanding, \( f(x) = a(x^2 + x - 6) \).

📌 Substitute \( x = 1 \): \( f(1) = a(1^2 + 1 - 6) = a(-4) \).

📌 Given \( f(1) = 6 \), then \( -4a = 6 \).

📌 Solving, \( a = -\frac{3}{2} \).

📌 A ball is thrown upward with an initial velocity of 20 m/s from a height of 5 meters. Its height after \( t \) seconds is modeled by \( h(t) = -5t^2 + 20t + 5 \). When does the ball hit the ground?

📌 Set \( h(t) = 0 \): \( -5t^2 + 20t + 5 = 0 \).

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