Multiple choice

Which one of the following condition will satisfy the zero product roots of the equation $(x - a)(x - b)$?

  1. $a\neq0$
  2. $b\neq0$
  3. $c\neq0$
  4. $a=0, b = 0$
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D Correct answer
Explanation

For the product (x - a)(x - b) to be zero, either x - a = 0 or x - b = 0. The roots are x = a and x = b. The condition for these roots to be zero is a = 0 and b = 0.

AI explanation

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero, meaning either x minus a equals zero or x minus b equals zero. For the roots of the expression itself to be zero, the expression must evaluate to zero when evaluated at x equals zero. Setting x to zero in the expression (x minus a)(x minus b) gives the product of negative a and negative b, which equals zero only if a equals zero and b equals zero. Therefore, the required condition is a equals zero and b equals zero.

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