Question

cheak whether the following are quadratic equation
(x + 2)^3 = 2x (x^2- 1)​

Answer 1

$\huge{\bf{\underline{\overline{\bf{Solution:-}\mid}}}}$

Given, equation is $\tt {(x + 2)}^{3} = 2x( {x}^{2} - 1)$

We need to check whether the given equation is quadratic or not.

Now,

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

$\implies\tt {x}^{3} + 3 {x}^{2} \times 2 + 3x \times {2}^{2} + {2}^{3} = 2 {x}^{3} - 2x$

$\implies\tt {x}^{3} + 6 {x}^{2} + 12x + 8 = 2 {x}^{3} - 2x$

$\implies\tt 2 {x}^{3} - {x}^{3} + 6 {x}^{2} + 12x + 2x + 8 = 0$

$\implies\tt {x}^{3} + 6 {x}^{2} + 14x + 8 = 0$

Since, we noticed that the degree of the polynomial is 3. So, the given equation is not a quadratic equation.

[A quadratic equation always has a degree of 2]