Question

16x²+40x+k is a perfect square polynomial, find k​

Answer 1

forstly we apply this formula on it

b²-4ac=0

a=16,b=40,c=k

now ,

(40)²-4×16×k=0

1600-64k=0

-64k=1600

-k=1600/64

-k=25

k=-25

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Answer 2

Answer:

k = 25

Step-by-step explanation:

16x^2+40x+k

it can be written as a square only when it is in the form of (a + b)^2

since it is to be written in form of (a + b)^2

16x^2 = a^2

(4x)^2 = a^2

cancel ^2 or exponent 2 from both sides

4x = a

similarly

(4x)^2 + 2(4x)(k^1/2) +k^1/2

as 2(4x)(k^1/2) = 40 [according to terms and relativity of given polynomial and formula]

8x(k^1/2) = 40x

k^1/2 = 40x/8x

k^1/2 = 5x/x

k = (5)^2

k = 25