Multiple choice

State whether True or False If we can factorize $ax^2 + bx + c, a\neq 0$, into a product of two linear factors, then the roots of the quadratic equation $ax^2 + bx + c = 0$ can be found by equating each factor to zero ?

  1. True

  2. False
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A Correct answer
Explanation

If a quadratic expression can be factored into (px + q)(rx + s) = 0, then by the zero product property, either px + q = 0 or rx + s = 0. This is the fundamental basis for solving quadratic equations by factoring.

AI explanation

According to the zero product property, if a quadratic expression ax^2 + bx + c is factorized into a product of two linear factors, the equation is satisfied when either factor equals zero. Therefore, equating each linear factor to zero will yield the roots of the quadratic equation. This statement is true.

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