Question

Find the value of k that would make the left side of the equation a perfect square trinomial.

9x² - kx + 4 = 0

Answer 1

Answer: k=±`12

Explanation:

`ax^2-bx+c=0\\\\9x^2-kx+4=0\\\\D=b^2-4ac\\\\a=9\ \ \ \ b=-k\ \ \ \ c=4\\\\D=0\\\\Hence,\\\\D=(-k)^ 2-4(9)(4)=0\\\\k^2-144=0\\\\k^2=144\\\\k^2=12^2`

Extract the square root of both parts of the equation:

`k=б√(12^2) \\\\k=б12`

Answer 2

• k = - 12 or k = 12

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A perfect square trinomial is:

• (a ± b)² = a² ± 2ab + b²

Given trinomial:

• 9x² - kx + 4 = 0

Show this as:

• (±3x)² - kx + (±2)² = 0

Compare and find possible values of k:

• k = - 2(±3)(±2) = ± 12