What is the solution for [tex]6r^2 - 10r - 24 = 0[/tex]?
Answer (2)
6 r 2 − 10 r − 24 = 0 a = 6 , b = − 10 , c = − 24 Δ = b 2 − 4 a c = ( − 10 ) 2 − 4 ⋅ 6 ⋅ ( − 24 ) = 100 + 576 = 676 r 1 = 2 a − b − Δ = 2 ⋅ 6 10 − 676 = 12 10 − 26 = 12 − 16 = − 3 4 r 2 = 2 a − b + Δ = 2 ⋅ 6 10 + 676 = 12 10 + 26 = 12 36 = 3 6 r 2 − 10 r − 24 = 6 ( r + 3 4 ) ( r − 3 ) = ( 6 r + 8 ) ( r − 3 ) A n s w er : 6 r 2 − 10 r − 24 = ( 6 r − 8 ) ( r − 3 )
The solutions to the equation 6 r 2 − 10 r − 24 = 0 are r = − 3 4 and r = 3 . These are found using the quadratic formula, resulting in one negative and one positive solution. The equation can also be expressed in factored form as ( 6 r + 8 ) ( r − 3 ) = 0 .
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