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X2 -5kx plus 25 the square of binomial. what is a possible value of k?
ChiomaUgochukwugp462...
k can be 2 or -2.
A binomial squared is: (a + b)² = a² + 2ab + b²
Given x² - 5kx + 25 = (a + b)² = a² + 2ab + b² we find:
a² = x² → a = ±x
2ab = -5kx
b² = 25 → b = ±5
If we let a = x, then:
2ab = 2xb = -5kx
→ 2 × ±5 = -5k
→ k = ±2
If k = 2 then the binomial is (x - 5)²
If k = -2 then the binomial is (x + 5)²
To be complete if a = -x, then:
If k = 2 then the binomial is (-x + 5)²
If k = -2 then the binomial is (-x - 5)²
which are the negatives of the binomials being squared.
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