The reduced form of $(2 x - 1)^{2} = x^{2} + 2$ is NOT a quadratic equation.

True

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False

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Solution

The correct option is B False
$(2 x - 1)^{2} = 4 x^{2} + 1 - 4 x$
So, the above equation reduces to $(2 x - 1)^{2} = x^{2} + 2$
$\Rightarrow 4 x^{2} + 1 - 4 x = x^{2} + 2$
$\Rightarrow 3 x^{2} - 4 x - 1 = 0$ This is a quadratic equation, because, the highest power of the variable, x, is 2

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Similar questions

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

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

Q. The standard form of quadratic equation

x^{2} = 2 x - 3

is _____ .

Question 2
Which of the following is not a quadratic equation?
(a) $2 (x - 1)^{2} = 4 x^{2} - 2 x + 1$
(b) $2 x - x^{2} = x^{2} + 5$
(c) ${(\sqrt{2} x + \sqrt{3})}^{2} = 3 x^{2} - 5 x$
(d) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{3}$

Question 2
Which of the following is not a quadratic equation?
(a) $2 (x - 1)^{2} = 4 x^{2} - 2 x + 1$
(b) $2 x - x^{2} = x^{2} + 5$
(c) ${(\sqrt{2} x + \sqrt{3})}^{2} = 3 x^{2} - 5 x$
(d) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{3}$

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The reduced form of (2x−1)2=x2+2 is NOT a quadratic equation.

The correct option is B False(2x−1)2=4x2+1–4x So, the above equation reduces to (2x−1)2=x2+2 ⇒4x2+1–4x=x2+2 ⇒3x2–4x–1=0 This is a quadratic equation, because, the highest power of the variable, x, is 2

The reduced form of $(2 x - 1)^{2} = x^{2} + 2$ is NOT a quadratic equation.

The correct option is B False
$(2 x - 1)^{2} = 4 x^{2} + 1 - 4 x$
So, the above equation reduces to $(2 x - 1)^{2} = x^{2} + 2$
$\Rightarrow 4 x^{2} + 1 - 4 x = x^{2} + 2$
$\Rightarrow 3 x^{2} - 4 x - 1 = 0$ This is a quadratic equation, because, the highest power of the variable, x, is 2