Check whether the following are quadratic equations

1) (x-3) (2x+1) = x(x+5)

2) x2+3x+1=(x-2)2

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Solution

(x - 3)(2x + 1) = x(x + 5)
⇒ 2x2 - 5x - 3 = x2 + 5x
⇒ x2 - 10x - 3 = 0
It is of the form ax2 + bx + c = 0.
Hence, the given equation is quadratic equation.

x2 + 3x + 1 = (x - 2)2
⇒ x2 + 3x + 1 = x2 + 4 - 4x
⇒ 7x - 3 = 0
It is not of the form ax2 + bx + c = 0.
Hence, the given equation is not a quadratic equation.

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