Which of the given equations are quadratic?

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

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2 x^{2} = - 1

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- x^{2} + x + 4 x^{2} = - 3

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- x + \frac{1}{2} = 0

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Solution

The correct options are
B $2 x^{2} = - 1$
C $- x^{2} + x + 4 x^{2} = - 3$
A quadratic equation in variable x is of the form $a x^{2} + b x + c = 0$ , where a, b, c are real numbers and a $\neq$ 0.

Equation $- x + x^{3} + 4 x^{2} = 0$ has third power of x and in equation $- x + \frac{1}{2} = 0$ , a=0. So, these equations are not in the above mentionaed form and hence are not quadratic.

Equation $2 x^{2} = - 1$ can be written as $2 x^{2} + 0 x + 1 = 0$ . It is of the above mentioned form and hence is quadratic.
Also, equation $- x^{2} + x + 4 x^{2} = - 3$ can be simplified and written as $3 x^{2} + x + 3 = 0$ and hence is quadratic.

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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) $x^{3} - 4 x^{2} - x + 1 = {(x - 2)}^{3}$

I s

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

a quadratic equation ?

Q. Check whether the following is quadratic equation.

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

Q. Check whether the following is a quadratic equation:

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

Q. Question 1(viii)
Check whether the following are quadratic equations:
(viii)

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

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