Question

Factorize the following eqation x2+2x+15

Answer 1

Hey there !

Solution:

Equation: x² + 2x + 15

a = 1, b = 2, c = 15

=> Discriminant = b² - 4ac

=> ( 2 )² - 4 ( 1 ) ( 15 )

=> 4 - 60

=> - 56

Since - 56 < 0, the equation will contain imaginary or unreal roots.

Hence the equation cannot be factored with normal real roots.

Hope my answer helped !

Answer 2

here is your answer OK


To solve this we want to factorise "x^2 -2x - 15" into the form (x+a)(x+b).
Now, if we expand (x+a)(x+b) we get x^2 + (a+b)x + ab. This means we have:

(x+a)(x+b) = x^2 + (a+b)x + ab = x^2 -2x - 15

Comparing these two equations we can see that we have (a+b)x = -2x and ab = -15. If we work through the factors of -15 (which are 1,-1,3,-3,5,-5,15,-15) we can see that we should pick a and b equal to 3 and -5.

So we have factorised the equation in the question to get:

x^2 -2x - 15 = (x+3)(x-5) = 0

Since any number times zero is equal to zero, we can see either x+3=0 or x-5=0. If we solve these equations we then get the solutions: x=-3 or x=5