Is x-3-4x-2-x-1-x-2-3 a quadratic equation- Maths Q-A

Find whether the given equation is a quadratic or not :⇒x^3 4x^2 x+1=(x 2)^30ex0ex⇒x^3 4x^2 – x + 1 = x^3 – 8 – 6x^2 + 12xBringing all the like terms to one sid ...

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Byju's Answer

Standard XII

Mathematics

Definition of Functions

Is x^3-4x^2-x...

Question

Is $x^{3} - 4 x^{2} - x + 1 = {(x - 2)}^{3}$ a quadratic equation?

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Solution

Find whether the given equation is a quadratic or not :
$\Rightarrow x^{3} - 4 x^{2} - x + 1 = {(x - 2)}^{3} \Rightarrow x^{3} - 4 x^{2} - x + 1 = x^{3} - 8 - 6 x^{2} + 12 x$
Bringing all the like terms to one side of the equation, we get,
$\Rightarrow x^{3} - x^{3} - 4 x^{2} + 6 x^{2} - x - 12 x + 1 + 8 = 0$
$\Rightarrow 2 x^{2} - 13 x + 9 = 0$
Thus the above equation is a polynomial of degree $2$ .
Hence, the given equation is a quadratic equation.

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Similar questions

Check whether the following are quadratic equations :
(i) ${(x + 1)}^{2} = 2 (x - 3)$
(ii) $x^{2} - 2 x = (- 2) (3 - x)$
(iii) $(x - 2) (x + 1) = (x - 1) (x + 3)$
(iv) $(x - 3) (2 x + 1) = x (x + 5)$
(v) $(2 x - 1) (x - 3) = (x + 5) (x - 1)$
(vi) $x^{2} + 3 x + 1 = {(x - 2)}^{2}$
(vii) ${(x + 2)}^{3} = 2 x (x^{2} - 1)$
(viii) $x^{3} - 4 x^{2} - x + 1 = {(x - 2)}^{3}$

Q. Which of the following are quadratic equations?
11 =

-

4x²

-

x³

I s

x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3}

a quadratic equation ?

Q. Check whether the following is a quadratic equation:

x^{3} - {4 x}^{2} - x + 1 = {(x - 2)}^{3}

Q. Check whether the following is quadratic equation.

x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3}

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Is x3−4x2−x+1=(x−2)3 a quadratic equation?

Is $x^{3} - 4 x^{2} - x + 1 = {(x - 2)}^{3}$ a quadratic equation?