Question

if 4x^2-12x+k is a perfect square,find the numerical value of k

Answer 1

Hi there!

According to given condtn. :-
4x² - 12x + k = (a - b)² = a² - 2ab + b²

Here,

♦
a² = 4
[ Squaring botg sides. ]

a = √4 = 2

♦
2ab = -12

2(2)b = -12

b = -12 / 4

b = 3

Finally,

♦ b² = k

(3)² = k

k = 9

Hence, The required answer is :-
Numerical value of k = 9

Hope it helps! :)

Answer 2

Answer :

Now,

4 x² - 12 x + k

= ( 2 x )² - ( 2 × 2 x × 3 ) + 3² - 3² + k

= ( 2 x - 3 )² + ( k - 9 ), since 3² = 9

Thus, the given polynomial be a perfect square is

k - 9 = 0

i.e., k = 9

Therefore, the numerical value of k is 9.

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