(a) find all zeros of the function (b) write the polynomial as a product of linear factors, (c) use your factorizatoin to determine the x-intercepts of the graph of the function.
#27.) f(x)= x^2-14x+36
I'm not sure how to work it out so any help would be very, very much appreciated. Person with most answers and worked out understandably will receive the 10 points. Thanks all, for trying, and helping my future!
2007-10-05 13:23:11 · 1 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
"zeros of the function" is the same as roots. To find them, we factor the quadratic and come up with the two factors "products of linear factors". The x-intercepts occur at the zero's, since if one factor is (x+b), then (x+b)=0 and x=-b. With all that said, the numbers, when multiplied to =36 must be negative, since the coefficient of x^2 is positive. Also their absolute sum is 14. However, this doesn't appear to happen with integers, so we punt and solve this a different way.
That is, by completing the square. If we had x^2-14x+49, this would factor to (x-7)^2. But we can create this with something "left over". So we write
x^2-14x+49-13. Then with some rearrangement, we have (x-7)^2= +/- sqrt(13) and x= 7+/-sqrt(13).
So those are your zeros and the x coordinates for the x-intercept. The product would be
[x-(7-sqrt(13))] and [x+(7+sqrt(13))].
2007-10-05 13:40:22 · answer #1 · answered by cattbarf 7 · 0⤊ 0⤋