Question

for what value of k the expression 4x^2 + 20x + k is a perfect square

Answer 1

Heya!!✋

Here is your answer.

4x² + 20x + k

=> (2x)² + 2 × 2x × 5 + k

=> (2x)² + 2 × 2x × 5 + (5)² [(a + b)² = a² + 2ab + b²]

=> (2x + 5)²

So, the value of k is 5² = 25

Hope it will help you..

Answer 2

Answer: k=25

Step-by-step explanation: another way of looking at it is by factoring

we can factor a binomial by opening two sets of brackets

( )( )

We have to put in our x value in the first place in the brackets

The factors of 4x^2 are 4x and 1x or 2x and 2x

Through trial and error we can figure out the first value in the brackets has to be 2x

(2x )(2x )

Know we need to focus on the value of k

We know that it’s value in the first bracket needs to be multipled by the x value in the second bracket and that it’s value in the second bracket needs to be multiplied by the x value in the first bracket

We also know that the number in the first and second bracket need to be the same because k is a perfect square

And we know that the first k value by first x value plus the second k value by the second x value must equal 20

This mean that the k.2x=10x

Divide both sides by 2x and the value that must go in the bracket is 5

(2x 5)(2x 5)

However we know that the two fives are factors of k which means k equals 25