I think this attachment will help you
To have roots as described, that means we have the following factors: From multiplicity 2 at x=1 has (x-1)^2 as its factor From multiplicity 1 at x=0 has x as a factor From multiplicity 1 at x = -4 has a factor of x+4 Putting these together we get that P(x) = A (x) (x+4) (x-1)^2 Multiply these out and find P(x) = A (x^2 + 4x) (x^2 - 2x + 1) A ( x^4 - 2x^3 + x^2 + 4x^3 - 8x^2 + 4x ) Combine like terms and find P(x) = A (x^4 + 2x^3 - 7x^2 + 4x) To find A, we use the point they gave us (5, 72) P(5) = A [ (5)^4 + 2(5)^3 - 7(5)^2 + 4(5) ] = 72 A [ 625 + 250 - 175 + 20 ] = 72 A [ 720 ] = 72 Divide both sides by 720 and find that A = 0.1 Final answer: P(x) = 0.1 ( x^4 + 2x^3 - 7x^2 + 4x) or P(x) = 0.1 x^4 + 0.2 x^3 - 0.7x^2 + 0.4x
S1 = speed of boat 1
<span> t1 = time to do 1400 meters (boat 1) </span>
S1*t1 = 1400
<span><span>S2 </span>= speed of boat 2 </span>
1400 + S2*t1 = X
t2 = time to do X + 600 (boat 2)
S1*t2 = X + 600
S2*t2 = 2X - 600
S1 = 1400/t1
S2 = (X-1400)/t1
<span>T = t2/t1 </span>
1400*T = X + 600
X*T - 1400*T = 2X - 600
X = 3600 meters
<span> River is 3600 meters wide</span>
Answer: (9,-10) or x=9...y=-10
