Question 1(viii)
Check whether the following are quadratic equations:
(viii) $x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3}$

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Solution

(viii) $x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3} \Rightarrow x^{3} - 4 x^{2} - x + 1 = x^{3} - 8 - 6 x^{2} + 12 x \Rightarrow 2 x^{2} - 13 x + 9 = 0$
It is of the form $a x^{2} + b x + c = 0$
Hence, the given equation is quadratic equation.

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Similar questions

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}

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. Check whether the following are Quadratic equations

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

Q. Check whether the following is quadratic equation.

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

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Roots of Quadratic Equation

Standard X Mathematics

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Question 1(viii) Check whether the following are quadratic equations: (viii) x3−4x2−x+1=(x−2)3

(viii) x3−4x2−x+1=(x−2)3⇒x3−4x2−x+1=x3−8−6x2+12x⇒2x2−13x+9=0 It is of the form ax2+bx+c=0 Hence, the given equation is quadratic equation.

Question 1(viii)
Check whether the following are quadratic equations:
(viii) $x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3}$

(viii) $x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3} \Rightarrow x^{3} - 4 x^{2} - x + 1 = x^{3} - 8 - 6 x^{2} + 12 x \Rightarrow 2 x^{2} - 13 x + 9 = 0$
It is of the form $a x^{2} + b x + c = 0$
Hence, the given equation is quadratic equation.