Question

2x^2-6x+5 Can be written in the form of a(x-b)^2 , where a, b and c are positive numbers work out the values of a, b and c Please show how you get the answer and thank you so much for helping :)

Answer 1

Loka like your question has a(x-b)^2 + c

Answer:

a = 2, b = 3/2 and c = 1/2

Step-by-step explanation:

Given expression, 2x^2 - 6x + 5, which is equal to a( x - b )^2 + c

= > 2x^2 - 6x + 5 = a( x - b )^2 + c

In RHS, x has co-efficient 1, so to make conditions same on LHS -

= > 2[ x^2 - 3x + (5/2) ] = a( x - b )^2 + c

Now, solving LHS-

= > 2[ x^2 - 2(3/2)x + (5/2) ]

= > 2[ x^2 - 2(3/2)x + (3/2)^2 - (3/2)^2 + (5/2) ]

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

= > 2[ ( x - 3/2 )^2 + ( - 9 + 10 )/4 ]

= > 2[ ( x - 3/2 )^2 + 1/4 ]

= > 2( x - 3/2 )^2 + 1/2

On comparing,

a = 2

b = 3/2

c = 1/2