Question

If 2x2 – 13x + 20 = (2x – 5)(x – 4), which equation(s) should be solved to find the roots of 2x2 – 13x + 20 = 0? Check all that apply.

A. 2x – 5 = 0
B. x + 4 = 0
C. 2x – 5 = x – 4
D. 2x + 5 = 0
E. x – 4 = 0

Answer 1

2x^2 – 13x + 20
= (2x – 5)(x – 4)

to find roots of 0 then (2x – 5)(x – 4) = 0
then (2x – 5) = 0 and (x – 4) = 0

answer
A. 2x – 5 = 0
E. x – 4 = 0

Answer 2

Hence, the correct options are:

A. 2x-5 = 0

and E. x-4 = 0

Explanation:

We are given a factorization of a polynomial function as:

`2x^2-13x+20=(2x-5)(x-4)`

The roots of the equation are the possible value of x such that the polynomial function is zero at that point.

i.e. we have to find x such that:

`2x^2-13x+20=0`

which could also be written as:

`(2x-5)(x-4)=0`

Hence, the equation that satisfy this equation is:

• 
  `2x-5=0`
• 
  `x-4=0`

Hence, the correct options are:

A. 2x-5 = 0

and E. x-4 = 0