Question

Check whether the equation x^3-4x^2+1=(x-2)^2 is quadratic or not

Answer 1

Answer:

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Answer 2

x^3 – 4x^2 – x + 1 = (x – 2)^3

We have:

x3 – 4x2 – x + 1 = (x – 2)3

⇒ x3 – 4x2 – x + 1 = x3 + 3x2(– 2) + 3x(– 2)2 + (– 2)3

⇒ x3 – 4x2 – x + 1 = x3 – 6x2 + 12x – 8

⇒ x3 – 4x2 – x – 1 – x3 + 6x2 – 12x + 8 = 0

2x2 – 13x + 9 = 0

Since 2x2 – 13x + 9 is a quadratic polynomial

∴ x3 – 4x2 – x + 1 = (x – 2)3 is a quadratic equation.