Question

Find a cubic function with the given zeros. 3, -4, 7

Answer 1

let's try to construct ax^3+bx^2+cx+d, then x=3=> 27+9b+3c+d=0; x=-4 => -81a+16b-4c+d=0; x=7=> 343a+49b+7c+d=0; now let's solve them simultanesouly

Answer 2

we should find a,b,c which makes it true

Answer 3

Ok f(x) = x3 - 6x2 + 19x + 84?

Answer 4

@barbillus

Answer 5

oops i solved it wrong

Answer 6

should be 235a+42b+14c=0

Answer 7

These are my options f(x) = x3 - 6x2 - 19x + 84

f(x) = x3 - 6x2 - 19x - 84

f(x) = x3 + 6x2 - 19 + 84

f(x) = x3 - 6x2 + 19x + 84

Answer 8

ok.. if you are given the options, i will tell you sth very useful: remember: in a cubic equation ax^3+bx^2+cx+d, the sum of the values which make the equation 0 = -b/a, and the multiplication of the values which make the equation 0 = -d/a

Answer 9

so you have 3, -4, and 7: 3-4+7=6 should be -b/a, and 3*(-4)*7=-84 should be -d/a

Answer 10

then the last option is true

Answer 11

since -(-6)/1 = 6 and -(84)/1 = -84 in the last choice

Answer 12

so the answer is f(x) = x3 - 6x2 + 19x + 84
??

Answer 13

yeah

Answer 14

Thank you :)