Find all roots of the polynomial function \( F(x) = x^2 - 2x - 24 \).

f ( x ) = x 2 − 2 x − 24 = x 2 + 4 x − 6 x − 24 = x ( x + 4 ) − 6 ( x + 4 ) = = ( x + 4 ) ( x − 6 ) f ( x ) = 0 ⇔ ( x + 4 ) ( x − 6 ) = 0 . ⇔ x + 4 = 0 or x − 6 = 0 . ⇔ x = − 4 or x = 6

Answered by kate200468 | 2024-06-10

f ( x ) = x 2 − 2 x − 24 x 2 − 2 x − 24 = 0 F a c t or i z a t i o n : x 2 + 4 x − 6 x − 24 = 0 x ( x − 6 ) + 4 ( x − 6 ) = 0 ( x + 4 ) ( x − 6 ) = 0 x = − 4 or x = 6

Answered by luana | 2024-06-10

The roots of the polynomial function F ( x ) = x 2 − 2 x − 24 are x = 6 and x = − 4 . This is found by factoring the quadratic equation into ( x − 6 ) ( x + 4 ) and setting each factor to zero. Solving these equations leads to the roots of the function.
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Answered by kate200468 | 2025-06-17