Question

the value of k for which the (x^2 +4x+k) is a perfect square

Answer 1

Given:

• A quadratic polynomial is given to us.
• The polynomial is (x²+4x+k) .

To Find:

• The value of k for which the given polynomial is a whole square.

Answer:

We are here given a quadratic polynomial which is x² + 4x + k .

We already know that the standard form of a quadratic polynomial is k[ax²+bx+c] , where k is a constant . When we will equate this with 0 , it will be called as quadratic equⁿ .

The Discriminant of quadratic equation is b²-4ac .

Now it will be a whole square if and only if the Discriminant is equal to 0.

i.e. b² - 4ac = 0.

On substituting the respective values ,

=> (4)² - 4× 1 × k = 0.

=> 16 - 4k = 0.

=> 4k = 16.

=> k = 16/4.

=> k = 4 .

Hence the required answer is k = 4.

Answer 2

Step-by-step explanation:

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