Multiple choice

$\displaystyle a^2x^2 - 3abx + 2b^2 $= 0 then $x = \cfrac{a}{b}\ and\ x = \cfrac{b}{a}$ are the roots of the equation.

  1. True

  2. False

  3. Ambiguos

  4. Can't say
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Factoring gives (ax - b)(ax - 2b) = 0, so the roots are b/a and 2b/a, assuming a and b are nonzero. Thus, a/b and b/a are not generally both roots.

AI explanation

To find the roots of a^2x^2 - 3abx + 2b^2 = 0, we can factor the quadratic expression by splitting the middle term as a^2x^2 - 2abx - abx + 2b^2 = 0. Factoring by grouping yields ax(ax - 2b) - b(ax - 2b) = 0, which simplifies to (ax - b)(ax - 2b) = 0. This gives the actual roots as x = b/a and x = 2b/a, making the provided statement false.

Keep practicing — related questions