Question: Use the discriminant to find the nature of the solutions of the given quadratic equation.
10x² + 8x + 9 = 0

A ) two real, irrational, unequal numbers
B ) two complex conjugate numbers
C ) two real, rational, unequal numbers
D ) one real, rational number (double)

Steps to derive

1 10x² + 8x + 9 = 0

2 a = 10, b = 8, c = 9
 [Compare with ax² + bx + c = 0.]

3 b² - 4ac = 64 - 4(10)(9)
 [Substitute and simplify.]

4 = - 296
 [Simplify.]

5 b² - 4ac < 0. So, the solutions are two complex conjugate numbers.



Hence the right answer is Option B

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