Question

Determine if each equation will have 0, 1, or 2 solutions. Equation A: x(x−3)=0 This equation has ____ solutions because... Equation B: x2=−81 This equation has ____ solutions because... Equation C: (x−1)(x−1)=0 This equation has ____ solutions because...

Answer 1

See below

Explanation:

Given the expression

x(x-3) = 0

This can be written as x = 0 and x - 3 = 0

x = 0 and x = 0+3

x = 0 and x = 3

Hence the equation has 2 solutions since it is a quadratic equation

B) Given x^2 = -81

Take the square root of both sides

√x² = ±√-81

x =±√-81

Note that √-1 = i

x = ±9i

x = 9i and -9i

Hence this equation has 2 solutions because of its quadratic nature

C) (x−1)(x−1)=0

x - 1 = 0 and x = 1 = 0

x = 1 twice

Hence this equation has 1 solution because of its repitition of root