Question

fill in the missing term, making the perfect trinomial square:

${x}^{2} - ? + 25$

Answer 1

Hola Friend ✋✋✋

Let 'bx' be in the place of ?

your question is

x² - bx + 25

We can use discriminant(D) here

If this polynomial is perfect trinomial then D = 0

D = b² - 4ac = 0

b = b

a = 1

c = 25


D = b² - 4 × 1 × 25 = 0

b² - 100 = 0

b² = 100

b = √100 = ± 10...

So perfect trinomial is

x² - 10x + 25

or x² + 10x + 25


Hope it helps

Answer 2

HELLO DEAR,

General form for a perfect (binomial) square:

(x+a)² = x²+2xa +a²-----(1)

here,

given that:-

x² + (-2ax) +25-----(2)

comparing --(1) and --(2)

a² = 25

=> a = +- 5

then the Equation is:

2ax = 2×(-5) × X = -10x

or

2ax = 2×5× X = 10X

hence the Equation is

x²-10x +25

----------------------or-----------------------

x² + 10x +25



I HOPE ITS HELP YOU DEAR,
THANKS