Which of the following equations are quadratic?

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

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

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(5 x^{2} + 2 x) - (7 + 5 x^{2}) = x^{2} + 2

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

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Solution

The correct options are
A $(x^{2} + 1)^{2} = x^{4}$
C $(5 x^{2} + 2 x) - (7 + 5 x^{2}) = x^{2} + 2$
The standard form of any quadratic equation is $a x^{2} + b x + c = 0$ ,
where a, b, c [coefficients] are real numbers and $a \neq 0$ [a is called the leading coefficient].

Option A: $(x^{2} + 1)^{2} = x^{4}$
$\Rightarrow x^{4} + 2 x^{2} + 1 = x^{4}$
$\Rightarrow 2 x^{2} + 1 = 0$ ; This is a quadratic equation.

Option B: $(x + 1)^{2} = x^{2}$
$\Rightarrow x^{2} + 2 x + 1 = x^{2}$
$\Rightarrow 2 x + 1 = 0$ ; This is a linear equation.

Option C: $(5 x^{2} + 2 x) - (7 + 5 x^{2}) = x^{2} + 2$
$\Rightarrow 2 x - 7 = x^{2} + 2$
$\Rightarrow x^{2} - 2 x + 9 = 0$ ; This is a quadratic equation.

Option D: $(x + 2)^{3} = 4 - x^{3}$
$\Rightarrow x^{3} + 6 x^{2} + 12 x + 8 = 4 - x^{3}$
$\Rightarrow 2 x^{3} + 6 x^{2} + 12 x + 4 = 0$
It's not a quadratic equation, it's a cubic equation as the highest power of x is of degree ‘3’.

Suggest Corrections

Similar questions

Which of the following is the reduced form of the equation $(x - 2)^{3}$ = $(2 x - 1)^{2} + x^{3}$ ?

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. What is/are the correct step(s) to solve the following equation?

2 x + 7 = 12 - 3 x

Q. If

α, β, γ

are the zeroes of

x^{3} - 5 x^{2} - 2 x + 24

and

α β = 12

, then

γ =

\frac{x^{3} + x^{2} + 2 x - 12}{x - 3}

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