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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Solution

The answer is (d).
a) Given that, $x^{2} + 2 x + 1 = (4 - x)^{2} + 3$
$\Rightarrow x^{2} + 2 x + 1 = 16 + x^{2} - 8 x + 3$
$\Rightarrow 10 x - 18 = 0$
Which is not of the form $a x^{2} + b x + c$ , a $\neq$ 0. Thus the equation is not a quadratic equation.
b) Given that, $- 2 x^{2} = (5 - x) (2 x - \frac{2}{5})$
$\Rightarrow - 2 x^{2} = 10 x - 2 x^{2} - 2 + \frac{2 x}{5}$
$\Rightarrow 50 x + 2 x - 10 = 0$
$\Rightarrow 52 x - 10 = 0$
Which is also not a quadratic equation.
c) Given that, $(k + 1) x^{2} + \frac{3}{2} x = 7, w h e r e k - = - 1$
$k = - 1$
$\Rightarrow x^{2} (- 1 + 1) \frac{3}{2} + x = 7$
$\Rightarrow 3 x - 14 = 0$
Which is also not a quadratic equation.
d) Given that, $x^{3} - x^{2} = (x - 1)^{3}$
$x^{3} - x^{2} = x^{3} - 3 x^{2} (1) + 3 x (1)^{2} - (1)^{3}$
$[∴ (a - b)^{3} = a^{3} - b^{3} + 3 a b^{2} - 3 a^{2} b]$
$x^{3} - x^{2} - x^{3} + 3 x^{2} - 3 x + 1 = 0$
$2 x^{2} - 3 x + 1 = 0$
Which represents a quadratic equation because it has the quadratic form.

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Similar questions

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

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

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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Question 1 Which of the following is a quadratic equation? (a) x2+2x+1=(4–x)2+3 (b) −2x2=(5−x)(2x−25) (c) (k+1)x2+32 x=7, where k−=−1 (d) x3−x2=(x−1)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) $x^{3} - x^{2} = (x - 1)^{3}$