Question

What is the square root of 16x⁴-24x³+25x²-12x+4

Answer 1

Answer:

Square root will be of the form a$x^{2}$ + bx + c

$(ax^2 + bx + c)^2 = 16x^4 + 24x^3 + 25x^2 - 12x +4$

$a^2x^4 + b^2x^2 + c^2 + 2acx^2 + 2bcx + 2abx^3$ = 16x⁴-24x³+25x²-12x+4

$x^4(a^2)+x^3(2ab)+x^2(2ac+b^2)+x(2bc) + c^2$ = 16x⁴-24x³+25x²-12x+4

Thus, we get

$a^2=16$

$2ab=-24$

$2ac + b^2=25$

$2bc = -12$

$c^2=4$

so,

a = +4 or -4

b = -3 or +3

c = +2 or -2

Therefore the square root is $4x^2-3x+2$ or $-4x^2+3x-2$

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