Decide which of the following are quadratic equations?i 9y2 + 5 = 0ii

1.	Decide which of the following are quadratic equations?i 9y2 + 5 = 0ii. m3 – 5m2 + 4 = 0iii. (l + 2)(l – 5) = 0
Answer» i. In the equation 9y² + 5 = 0, [y] is the only variable and maximum index of the variable is [2]. ∴ It [is] a quadratic equation. ii. In the equation m³ – 5m² + 4 = 0, [m] is the only variable and maximum index of the variable is not 2. ∴ It [is not] a quadratic equation. iii. (l + 2)(l – 5) = 0 ∴ l(l – 5) + 2(l – 5) = 0 ∴ l² – 5l + 2l – 10 = 0 ∴ l² – 3l – 10 = 0. In this equation [l] is the only variable and maximum index of the variable is [2] ∴ it [is] a quadratic equation.

Decide which of the following are quadratic equations?i 9y2 + 5 = 0ii. m3 – 5m2 + 4 = 0iii. (l + 2)(l – 5) = 0

Answer»

i. In the equation 9y² + 5 = 0, [y] is the only variable and maximum index of the variable is [2].

∴ It [is] a quadratic equation.

ii. In the equation m³ – 5m² + 4 = 0, [m] is the only variable and maximum index of the variable is not 2.

∴ It [is not] a quadratic equation.

iii. (l + 2)(l – 5) = 0

∴ l(l – 5) + 2(l – 5) = 0

∴ l² – 5l + 2l – 10 = 0

∴ l² – 3l – 10 = 0.

In this equation [l] is the only variable and maximum index of the variable is [2]

∴ it [is] a quadratic equation.