Question

Decide which of the following are quadratic equations.
(1) x² + 5x – 2 = 0
(2) y² = 5y – 10
(3) $y^2+\frac{1}{y}=2$
(4) $x+\frac{1}{x}=-2$
(5) (m + 2) (m – 5) = 0
(6) m³ + 3m² – 2 = 3m³

Answer 1

(1) x² + 5x – 2 = 0
Only one variable x.
Maximum index = 2
So, it is a quadratic equation.

(2) y² = 5y – 10
Only one variable y.
Maximum index = 2
So, it is a quadratic equation.

(3) $y^2+\frac{1}{y}=2$
$\Rightarrow y^3+1=2y$
Only one variable y.
Maximum index = 3
So, it is not a quadratic equation.

(4) $x+\frac{1}{x}=-2$
$\Rightarrow x^2+1=-2x$
Only one variable x.
Maximum index = 2
So, it is a quadratic equation.

(5) (m + 2) (m – 5) = 0
$\Rightarrow m^2-3m-10=0$
Only one variable m.
Maximum index = 2
So, it is a quadratic equation.

(6) m³ + 3m² – 2 = 3m³
Only one variable m.
Maximum index = 3
So, it is not a quadratic equation.