Question

Check whether the following are quadratic equations:
(i) 3 x ² – 4 =0
(ii)(x+1)(x+3)=0
(iii)(2x+1)(3x+2)=6(x-1)(x-2)
(iv)16x^2-3=(2x+5)(5x-3)

Answer 1

Answer:

1)  3 x ² – 4 = 0

It is a quadratic equation because it is of degree 2.

2) (x+1) (x+3) = 0

On simplifying, we get,

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

It is also a quadratic equation.

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

On simplifying, we get,

$6x^{2} +4x + 3x +2 = 6(x^{2} -3x+ 2)\\6x^{2} +4x + 3x +2 = 6x^{2} -18x +12\\\4x + 3x +2 = -18x +12\\ 7x+18x +2-12 =0\\25x -10 =0 \\simplifying further,\\5x - 2 =0$

It is not a quadratic equation

4) 16x^2 - 3 = (2x+5) (5x-3)

$16x^2-3=(2x+5)(5x-3)\\16x^2-3 = 10x^{2} -6x +25x -15 \\6x^{2} - 19x + 12 = 0$

It is also a quadratic equation

Thank you!