Multiple choice

State the following statement is True or False The following equation has real roots. $5x^2+ 23x- 10 = 0$

  1. True

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

For a quadratic equation ax^2 + bx + c = 0, real roots exist if the discriminant D = b^2 - 4ac >= 0. Here, D = 23^2 - 4(5)(-10) = 529 + 200 = 729, which is positive, so the roots are real.

AI explanation

The nature of the roots is determined by the discriminant, b^2 - 4ac, where a = 5, b = 23, and c = -10. Calculating this gives 23^2 - 4(5)(-10) = 529 + 200 = 729. Since the discriminant is positive, the equation definitely has real roots.

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