Which of the following is a quadratic equation-a x 2-3 x-2-0b x-1 x-x 2c x 2-1 - 2-5d 2 x 2-5 x-x-1 2

(d) 2x2 #160; #160; #160;5x #160;= #160;(x #160; #160;1)2 A #160;quadratic #160;equation #160;is #160;the #160;equation #160;with ...

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Standard X

Mathematics

Arithmetic Progression

Which of the ...

Question

Which of the following is a quadratic equation?
(a) $x^{2} - 3 \sqrt{x} + 2 = 0$
(b) $x + \frac{1}{x} = x^{2}$
(c) $x^{2} + \frac{1}{x^{2}} = 5$
(d) $2 x^{2} - 5 x = (x - 1)^{2}$

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Solution

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

$A quadratic equation is the equation with degree 2 . ∵ 2 x^{2} - 5 x = {(x - 1)}^{2} \Rightarrow 2 x^{2} - 5 x = x^{2} - 2 x + 1 \Rightarrow 2 x^{2} - 5 x - x^{2} + 2 x - 1 = 0 \Rightarrow x^{2} - 3 x - 1 = 0, which is a quadratic equation$

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

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

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)

1. Check if $($ x-2 $)^{2}$ = $x^{2}$ + 5x + 6. Is a quadratic equation?

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Which of the following is a quadratic equation? (a) x2-3x+2=0 (b) x+1x=x2 (c) x2+1x2=5 (d) 2x2 - 5x=(x-1)2

(d) 2x2 - 5x = (x - 1)2 A quadratic equation is the equation with degree 2.∵ 2x2 − 5x = (x − 1)2⇒ 2x2 − 5x = x2 − 2x + 1⇒ 2x2 − 5x − x2 + 2x − 1 = 0⇒ x2 − 3x − 1 = 0, which is a quadratic equation

Which of the following is a quadratic equation?
(a) $x^{2} - 3 \sqrt{x} + 2 = 0$
(b) $x + \frac{1}{x} = x^{2}$
(c) $x^{2} + \frac{1}{x^{2}} = 5$
(d) $2 x^{2} - 5 x = (x - 1)^{2}$

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

$A quadratic equation is the equation with degree 2 . ∵ 2 x^{2} - 5 x = {(x - 1)}^{2} \Rightarrow 2 x^{2} - 5 x = x^{2} - 2 x + 1 \Rightarrow 2 x^{2} - 5 x - x^{2} + 2 x - 1 = 0 \Rightarrow x^{2} - 3 x - 1 = 0, which is a quadratic equation$