The value of n for which the expression $9 x^{4} - 12 x^{3} + n x^{2} - 8 x + 4$ becomes a perfect square is

12

No worries! We‘ve got your back. Try BYJU‘S free classes today!

16

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

18

No worries! We‘ve got your back. Try BYJU‘S free classes today!

24

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $16$
Let the equation be of the form $(a x^{2} + b x + c)^{2} = a^{2} x^{4} + b^{2} x^{2} + c^{2} + 2 a b x^{3} + 2 b x c + 2 a c x^{2}$
$a^{2} x^{4} + 2 a b x^{3} + (b^{2} + 2 a c) x^{2} + c^{2} + 2 b x c$ = $9 x^{4} - 12 x^{3} + n x^{2} - 8 x + 4$
Comparing the coefficients, $a = 3, c = 2$
$2 a b = - 12$
$b = - 2$
Therefore, $n = b^{2} + 2 a c$ $= 4 + 12 = 16$

Suggest Corrections

Similar questions

m - n x + 28 x^{2} + 12 x^{3} + 9 x^{4}

9 x^{4} + 12 x^{3} + 28 x^{2} + 16 x + 16

a

b

4 x^{4} - 12 x^{3} + 37 x^{2} + a x + b

\sqrt{9 x^{4} + 6 x^{3} - 5 x^{2} - m x + 1}

m

Which of the following operations can

convert the expression (x^{2} + \frac{8 x}{\sqrt{3}})

into a perfect square?

Join BYJU'S Learning Program