Given f(x) = x2 - px + q. Since f(x) is divisible by (x+a), by the Factor Theorem, f(-a) = 0.

May 16, 2026Mathematics

ScanSolve AI Answer

May 16, 2026

Answer

(-a)^2 - p(-a) + q = 0$$

Step 1: Apply the Factor Theorem to $f(x)$ . Given $f(x) = x^2 - px + q$ . Since $f(x)$ is divisible by $(x+a)$ , by the Factor Theorem, $f(-a) = 0$ . $f(-a) = (-a)^2 - p(-a) + q = 0$ $a^2 + pa + q = 0 \quad (1)$

Step 2: Apply the Factor Theorem to $g(x)$ . Given $g(x) = x^2 + lx + m$ . Since $g(x)$ is divisible by $(x+a)$ , by the Factor Theorem, $g(-a) = 0$ .

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Apply the Factor Theorem to f(x). Given f(x) = x^2 - px + q.

Asked on May 16, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 16, 2026

Step 1: Apply the Factor Theorem to f(x). Given f(x) = x^2 - px + q. Since f(x) is divisible by (x+a), by the Factor Theorem, f(-a) = 0. f(-a) = (-a)^2 - p(-a) + q = 0 a^2 + pa + q = 0 (1) Step 2: Apply the Factor Theorem to g(x). Given g(x) = x^2 + lx + m. Since g(x) is divisible by (x+a), by the Factor Theorem, g(-a) = 0. g(-a) = (-