Which of the following is not a quadratic equation?
[1 mark]

(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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Solution

The correct option is (d). [1 mark]

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 it has the quadratic form $a x^{2} + b x + c = 0$ , a $\neq$ 0
c) Given that, ${(\sqrt{2} x + \sqrt{3})}^{2} = 3 x^{2} - 5 x$
$\Rightarrow 2 x^{2} + 2 \sqrt{6} x + 3 = 3 x^{2} - 5 x$

$\Rightarrow x^{2} - (5 + 2 \sqrt{6}) x - 3 = 0$
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 does not represent a quadratic equation because it does not have the quadratic form $a x^{2} + b x + c = 0$ , a $\neq$ 0

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Similar questions

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

The expresssion $x^{4} + 4$ can be factorized as

Q. The expression x⁴ + 4 can be factorized as

(a) (x² + 2x + 2) (x² − 2x + 2)

(b) (x² + 2x + 2) (x² + 2x + 2)

(c) (x² − 2x − 2) (x²− 2x + 2)

(d) (x² + 2) (x² − 2)

Q. Write the discriminant of the following quadratic equations:

(i) 2x² − 5x + 3 = 0
(ii) x² + 2x + 4 = 0
(iii) (x − 1) (2x − 1) = 0
(iv) x² − 2x + k = 0, k ∈ R
(v)

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

(vi) x² − x + 1 = 0

Q. Which of the following are quadratic equations?

(i) x² + 6x − 4 = 0
(ii)

\sqrt{3} x^{2} - 2 x + \frac{1}{2} = 0

(iii)

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

(iv)

x - \frac{3}{x} = x^{2}

(v)

2 x^{2} - \sqrt{3 x} + 9 = 0

(vi)

x^{2} - 2 x - \sqrt{x} - 5 = 0

(vii) 3x² − 5x + 9 = x² − 7x + 3
(viii)

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

(ix) x² − 3x = 0
(x)

{(x + \frac{1}{x})}^{2} = 3 (x + \frac{1}{x}) + 4

(xi) (2x + 1) (3x + 2) = 6(x − 1) (x − 2)
(xii)

x + \frac{1}{x} = x^{2}, x \neq 0

(xiii) 16x² − 3 = (2x + 5) (5x − 3)
(xiv) (x + 2)³ = x³ − 4
(xv) x(x + 1) + 8 = (x + 2) (x − 2)

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Which of the following is not a quadratic equation? [1 mark] (a) 2(x−1)2=4x2−2x+1 (b) 2x−x2=x2+5 (c) (√2x+√3)2=3x2−5x (d) (x2+2x)2=x4+3+4x3

Which of the following is not a quadratic equation?
[1 mark]

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