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) ${(\sqrt{2} x + \sqrt{3})}^{3} = 3 x^{2} - 5 x$
(d) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{2}$

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Solution

a) Given that, $2 (x - 1)^{2} = 4 x^{2} 2 x + 1$
$\Rightarrow 2 (x^{2} + 1 - 2 x) = 4 x^{2} - 2 x + 1$
$\Rightarrow 2 x^{2} + 2 - 4 x = 4 x^{2} - 2 x + 1$
$\Rightarrow 2 x^{2} + 2 x - 1 = 0$
Which represents a quadratic equation because it has the quadratic form $a x^{2} + b x + c = 0, a \neq 0$
b) Given that, $2 x - x^{2} = x^{2} + 5$
$\Rightarrow 2 x 2 - 2 x + 5 = 0$
Which represents a quadratic equation because I has the quadratic form $a x^{2} + b x + c = 0$ , a $\neq$ 0
c) Given that, ${(\sqrt{2} x + \sqrt{3})}^{2} = 3 x^{2} - 5 x$
$\Rightarrow 2 x^{2} + 3 \sqrt{6} + x = 3 x^{2} - 5 x$
$\Rightarrow x^{2} - (5 + 2 \sqrt{6}) x - 3 = 0$
Which also represents a quadratic equation because it has the quadratic form $a x^{2} + b x + c = 0$ , a $\neq$ 0
d) Given that, $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{2}$
$\Rightarrow x^{4} + 4 x^{2} + 4 x^{3} = x^{4} + 3 + 4 x^{2}$
$\Rightarrow 4 x^{3} - 3 = 0$
Which is not of the form $a x^{2} + b x + c = 0$ , a $\neq$ 0. Thus, the equation is not quadratic. This is a cubic 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) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{3}$

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

Q. 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}

Which of the following is not a quadratic equation?
(i) $(\sqrt{2} x + \sqrt{3})^{2} = 3 x^{2} - 5 x$
(ii) $2 x - x^{2} = x^{2} + 5$
(iii) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{2}$

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

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Question 2 Which of the following is not a quadratic equation? (a) 2(x−1)2=4x2−2x+1 (b) 2x−x2=x2+5 (c) (√2x+√3)3=3x2−5x​​​​​​​ (d) (x2+2x)2=x4+3+4x2​​​​​​​

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) ${(\sqrt{2} x + \sqrt{3})}^{3} = 3 x^{2} - 5 x$
(d) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{2}$