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Byju's Answer

Standard XII

Mathematics

Quadratic Equation

Which of the ...

Question

Which of the following is/are quadratic equation?

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

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(x - 2) (x + 1) = (x - 1) (x + 3)

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

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

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Solution

The correct options are
A $(x + 1)^{2} = 2 (x - 3)$
C $x^{2} - 2 x = (- 2) (3 - x)$
D $(x + 2) (x - 2) = - x^{2}$
$(x + 1)^{2} = 2 (x - 3)$
$\Rightarrow x^{2} + 2 x + 1 = 2 x - 6$
$\Rightarrow x^{2} + 7 = 0$
This is a quadratic equation.

$(x - 2) (x + 1) = (x - 1) (x + 3)$
$\Rightarrow x^{2} - x - 2 = x^{2} + 2 x - 3$
$\Rightarrow 3 x - 1 = 0$
This is NOT a quadratic equation.

$x^{2} - 2 x = (- 2) (3 - x) \Rightarrow x^{2} - 2 x = - 6 + 2 x$
$\Rightarrow x^{2} - 4 x + 6 = 0$
This is a quadratic equation.

$(x + 2) (x - 2) = - x^{2} \Rightarrow x^{2} - 4 = - x^{2}$
$\Rightarrow 2 x^{2} - 4 = 0$
This is a quadratic equation.

Suggest Corrections

Similar questions

Check whether the following are quadratic equations :
(i) ${(x + 1)}^{2} = 2 (x - 3)$
(ii) $x^{2} - 2 x = (- 2) (3 - x)$
(iii) $(x - 2) (x + 1) = (x - 1) (x + 3)$
(iv) $(x - 3) (2 x + 1) = x (x + 5)$
(v) $(2 x - 1) (x - 3) = (x + 5) (x - 1)$
(vi) $x^{2} + 3 x + 1 = {(x - 2)}^{2}$
(vii) ${(x + 2)}^{3} = 2 x (x^{2} - 1)$
(viii) $x^{3} - 4 x^{2} - x + 1 = {(x - 2)}^{3}$

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)

Q. Which of the following are quadratic equation in x ?
(i)

x^{2} - x + 3 = 0

(ii)

2 x^{2} + \frac{5}{2} x - \sqrt{3} = 0

(iii)

\sqrt{2} x^{2} + 7 x + 5 \sqrt{2} = 0

(iv)

\frac{1}{3} x^{2} + \frac{1}{5} x - 2 = 0

(v)

x^{2} - 3 x - \sqrt{x} + 4 = 0

(vi)

x - \frac{6}{x} = 3

(vii)

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

(viii)

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

(ix)

{(x + 2)}^{3} = x^{3} - 8

(x)

(2 x + 3) (3 x + 2) = 6 (x - 1) (x - 2)

(xi)

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

Q. Which of the following equations is quadratic ?
(1)

x^{2} + 2 x + 11 = 0

(2)

x^{2} - 2 x + 5 = x^{2}

(3)

{(x + 2)}^{2} = 2 x^{2}

Write the discriminant of the following quadratic equations:
(i) $2 x^{2} - 5 x + 3 = 0$ (ii) $x^{2} + 2 x + 4 = 0$
(iii) $(x - 1) (2 x - 1) = 0$ (iv) $x^{2} - 2 x + k = 0, k ϵ R$
(v) $\sqrt{3} x^{2} + 2 \sqrt{2} x - 2 \sqrt{3} = 0$ (vi) $x^{2} - x + 1 = 0$

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Quadratic Equation

Standard XII Mathematics

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