Multiple choice

The roots of the following quadratic equation $9a^2b^2x^2$ - 24abcdx + $16c^2d^2$ = 0, a $\neq$ 0, b $\neq$ 0 are Real and equal.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The discriminant is (24abcd)^2 - 4(9a^2b^2)(16c^2d^2) = 576a^2b^2c^2d^2 - 576a^2b^2c^2d^2 = 0. A discriminant of 0 means the roots are real and equal.

AI explanation

The equation 9a^2b^2x^2 - 24abcdx + 16c^2d^2 = 0 is a perfect square of the form (3abx - 4cd)^2 = 0. This factors into two identical linear expressions, (3abx - 4cd)(3abx - 4cd) = 0. Setting the factor to zero gives a single real root, x = 4cd/3ab, repeated twice, so the roots are real and equal. The statement is True.

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