Question

What is the solution set to the equation (2x−4)(4x−5)=0

Answer 1

`\left \{ 2,(5)/(4) \right \}`

Explanation:

We know that for equation of type
`(x-a)(x-b)=0`, solutions are
`x=a\,,\,x=b` as both points x = a and x = b satisfy the equation (x-a)(x-b)=0

Given : equation (2x−4)(4x−5)=0

To find : Solution set of this equation .

Solution :

On dividing this equation by 2 and 4, we get

`\left ( (2x-4)/(2) \right )\left ( (4x-5)/(4) \right )=0\\\left ( x-2 \right )\left ( x-(5)/(4) \right )=0`

On comparing equation
`\left ( x-2 \right )\left ( x-(5)/(4) \right )=0` with
`\left ( x-a \right )\left ( x-b \right )=0`, we get
`a=2\,,\,b=(5)/(4)`

Therefore, solution set is
`\left \{ 2,(5)/(4) \right \}`