Question

2x²-6x+5 can be written in the form a(x -b)² + c where a, b and c are positive numbers. Find a,b and c.

Answer 1

a = 2, b =
`(3)/(2)` , c =
`(1)/(2)`

Explanation:

2x² - 6x + 5 ( factor out 2 from the first 2 terms )

= 2(x² - 3x) + 5

using the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² - 3x

= 2[(x² + 2( -
`(3)/(2)` )x + (-
`(3)/(2)` )² - (-
`(3)/(2)` )² ) ] + 5

= 2[(x -
`(3)/(2)` )² +
`(9)/(4)` -
`(9)/(4)` )] + 5

= 2(x -
`(3)/(2)` )² + 2(-
`(9)/(4)` ) + 5

= 2(x -
`(3)/(2)` )² -
`(9)/(2)` + 5

= 2(x -
`(3)/(2)` )² +
`(1)/(2)` ← in the form a(x - b)² + c

with a = 2 , b =
`(3)/(2)` , c =
`(1)/(2)`