Question

1. Write any two quadratic equations. 2. Decide which of the following are quadratic equations. (1) \( x^{2}+5 x-2=0 \) (2) \( y^{2}=5 y-10 \) (3) \( y^{2}+\frac{1}{y}=2 \) (4) \( x+\frac{1}{x}=-2 \) (5) \( (m+2)(m-5)=0 \) (6) \( m^{3}+3 m^{2}-2=3 m^{3} \)

Answer 1

Quadratic equation is a second degree polynomial equation. It's standard form is ax²+bx+c = 0

(2) (i) x²+5x-2 = 0 is a polynomial equation of degree 2.

∴ It is quadratic equation.

(ii) y² = 5y-10

⇒ y²-5y+10 = 0 is a polynomial equation of degree 2.

∴ It is quadratic equation.

(iii) y²+1/y = 2

⇒ y³+1 = 2y

⇒ y³-2y+1 = 0

which is a polynomial equation of degree 3.

∴ It is not a quadratic equation.

(iv) x+1/x = -2

⇒ x²+1 = -2x

⇒ x²+2x+1 = 0 which is a polynomial equation of degree 2.

∴ It is a quadratic equation.

(v) (m+2)(m-5) = 0

⇒ m²+2m-5m-10 = 0

⇒ m²-3m-10 = 0 which is a polynomial equation of degree 2.

∴ It is a quadratic equation is m.

(vi) m³+3m²-2 = 3m³

⇒ 2m³-3m²+2 = 0 which is a polynomial equation of degree 3.

∴ It is not a quadratic equation.