What are the factors of [tex]3x^2 + 7x - 20[/tex]?
Answer (2)
3 x 2 + 7 x − 20 = 0 a = 3 ; b = 7 ; c = − 20 Δ = b 2 − 4 a c x 1 = 2 a − b − Δ ; x 2 = 2 a − b + Δ Δ = 7 2 − 4 ⋅ 3 ⋅ ( − 20 ) = 49 + 240 = 289 ; Δ = 289 = 17 x 1 = 2 ⋅ 3 − 7 − 17 = 6 − 24 = − 4 ; x 2 = 2 ⋅ 3 − 7 + 17 = 6 10 = 3 5 3 x 2 + 7 x − 20 = 3 ( x + 4 ) ( x − 3 5 ) 3 x 2 + 7 x − 20 = 0 ⟺ x = − 4 ∨ x = 3 5
The quadratic 3 x 2 + 7 x − 20 can be factored as 3 ( x + 4 ) ( x − 3 5 ) . The roots of the equation are x = − 4 and x = 3 5 . This method involves using the quadratic formula to find factors.
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