Tom thinks of a number. He squares it, adds 3 times the original number and then subtracts 18. The result is 0. What two numbers could Tom have been thinking of?
Formulate the problem algebraically:x2+3x-18=0This is a factorisation problem. To find the solutions, factorise:-Factors of x2 are 1 and 1, so answer will take the form: (x +- ?)(x +- ?)=0-List pairs of factors of 18: (1,18), (2,9), (3,6). -When multiplied by factors of x2, find the factors of 18 that produce the x coeffcient: (3,6). -We now know factorised equation takes the form: (x +- 3)(x +- 6)=0-x coefficient is +3, so correct solution is +6 and -3 (6x+(-3x)=3x).-Factorised equation is (x-3)(x+6)=0-Equation holds when x=-6,3, so the two numbers Tom could have been thinking of are -6 and 3.
GH
