Which of the following is not a quadratic equation?
(a) $3 x - x^{2} = x^{2} + 5$
(b) $(x + 2)^{2} = 2 (x^{2} - 5)$
(c) $(2 x + 3)^{2} = 2 x^{2} + 6$
(d) $(x - 1)^{2} = 3 x^{2} + x - 2$

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Solution

The correct option is (c): $(2 x + 3)^{2} = 2 x^{2} + 6$
(a) $3 x - x^{2} = x^{2} + 5$
$3 x = 2 x^{2} + 5$
$2 x^{2} - 3 x + 5 = 0$ , is a quadratic equation.
(b) $(x + 2)^{2} = 2 (x^{2} - 5)$
$\Rightarrow x^{2} + 4 + 2 x = 2 x^{2} - 10$
$\Rightarrow x^{2} - 2 x - 14 = 0$ , is a quadratic equation.
(c) $(2 x + 3)^{2} = 2 x^{2} + 6$
$\Rightarrow 2 x^{2} + 9 + 2 \times 2 x \times 3 = 2 x^{2} + 6$
$\Rightarrow 12 x + 3 = 0,$ which is not a quadratic equation.
(d) $(x - 1)^{2} = 3 x^{2} + x - 2$
$\Rightarrow x^{2} + 1 - 2 x = 3 x^{2} + x - 2$
$\Rightarrow 2 x^{2} + 3 x - 3 = 0$ , is a quadratic equation.

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

Q. Which of the following is a quadratic equation?
(a)

x^{2} - 3 \sqrt{x} + 2 = 0

(b)

x + \frac{1}{x} = x^{2}

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x^{2} + \frac{1}{x^{2}} = 5

(d)

2 x^{2} - 5 x = (x - 1)^{2}

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 1
Which of the following is a quadratic equation?
(a) $x^{2} + 2 x + 1 = (4 - x)^{2} + 3$
(b) $- 2 x^{2} = (5 - x) (2 x - \frac{2}{5})$
(c) $(k + 1) x^{2} + \frac{3}{2} x = 7, w h e r e k = - 1$
(d) $x^{3} - x^{2} = (x - 1)^{3}$

Q. Which of the following is a quadratic equation?
(a)

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

(b)

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

(c)

2 x^{2} + 3 = (5 + x) (2 x - 3)

(d) None of these

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Which of the following is not a quadratic equation?(a) 3x−x2=x2+5(b) (x+2)2=2(x2−5)(c) (2x+3)2=2x2+6(d) (x−1)2=3x2+x−2

Which of the following is not a quadratic equation?
(a) $3 x - x^{2} = x^{2} + 5$
(b) $(x + 2)^{2} = 2 (x^{2} - 5)$
(c) $(2 x + 3)^{2} = 2 x^{2} + 6$
(d) $(x - 1)^{2} = 3 x^{2} + x - 2$