Which of the following is/are not a quadratic equation?

$x^{2} - 8 x + 5 = 0$

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$3 x^{2} - 4 = 0$

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$2 x = x^{2}$

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$x + 5 = 3$

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Solution

The correct option is D
$x + 5 = 3$

Standard form of a Quadratic Equation is $a x^{2} + b x + c = 0, a \neq 0$

$(i) x^{2} - 8 x + 5 = 0$ is in the standard form, so it is a quadratic equation.

$(i i) 3 x^{2} - 4 = 0$ is in the standard form, so it is a quadratic equation.

$(i i i) 2 x = x^{2} \Rightarrow x^{2} - 2 x = 0$ is in the standard form, so it is a quadratic equation.

$(i v) x + 5 = 3 \Rightarrow 0 x^{2} + x + 2 = 0$ which is not a quadratic equation because the coefficient of $x^{2} (a) = 0$ .

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Find the nature of the roots of the following quadratic equations:
(i) $2 x^{2} - 8 x + 5 = 0$

(ii) $3 x^{2} - 2 \sqrt{6} x + 2 = 0$
(iii) $5 x^{2} - 4 x + 1 = 0$

(iv) $5 x (x - 2) + 6 = 0$
(v) $12 x^{2} - 4 \sqrt{15} x + 5 = 0$

(vi) $x^{2} - x + 2 = 0$

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

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