Question

check whether the (x+2) ^3 = x^ 3 -4 is a quadratic equation or not.​

Answer 1

Solution :-

A quadratic polynomial is a one whose degree is 2 i.e. highest power of variable in the equation must be 2.

We are given equation,

⇒ ( x + 2 )³ = x³ - 4

By expanding it using the identity :

• ( a + b )³ = a³ + b³ + 3a²b + 3ab²

⇒ ( x + 2 )³ = x³ - 4

⇒ x³ + 8 + 6x² + 12x = x³ - 4

⇒ x³ - x³ + 8 + 6x² + 12x + 4 = 0

⇒ 6x² + 12x + 12 = 0

⇒ 6 ( x² + 2x + 2 ) = 0

⇒ x² + 2x + 2 = 0

Now, here we can see that the highest power of x in this equation, is 2. This implies that the given equation is a quadratic one.

More Information :-

Every quadratic equation is of the form :

• ax² + bx + c = 0 , a ≠ 0

Sum of zeroes of this quadratic equation is given by :

• Sum of zeroes = -b/a

Product of zeroes of equation is given by :

• Product of zeroes = c / a