Sum of roots

Question

2(x²-1)=7x+13 solve an sum of two roots

Answer 1

If a(x-b)(x-c)=0,

then ax^2 - a(b+c)x + bc = 0.

 

The sum of the two roots is the opposite of the coefficient of the linear term divided by the leading coefficient.

 

Tom's 3rd line is 2x^2 - 7x -15 = 0.

 

We can immediately say the sum of the roots is 7/2.

Answer 2

2(x^2 -1) = 7x + 13

2x^2 - 2 = 7x +13

2x^2 - 7x -15 = 0

 

Factoring we get

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

 

2X + 3 =0

 

2X = -3

X = -3/2

 

AND

 

x - 5 =0

x = 5