What is the positive difference of the roots of x² - 7x - 9 = 0?
- 3√5
- √85
- 14
- None of these
Explanation
To find the roots of the quadratic equation x² - 7x - 9 = 0:
Use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 1, b = -7, and c = -9:
x = (7 ± √((-7)² - 4(1)(-9))) / 2(1)
= (7 ± √(49 + 36)) / 2
= (7 ± √85) / 2
The two roots are:
x₁ = (7 + √85) / 2
x₂ = (7 - √85) / 2
The positive difference between the roots is:
|x₁ - x₂| = |((7 + √85) / 2) - ((7 - √85) / 2)|
= |(7 + √85 - 7 + √85) / 2|
= |2√85 / 2|
= √85
Related MCQs
- 2x² + 4 = 9x
- 2x² + 9 = 4x
- 2x² + 9 = 4x
- x² + 4 = 9x
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