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Answer :
Final answer:
The roots of the equation 5x³ + 45x² + 70x = 0 are -7 and -2.
Explanation:
This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 5, b = 45, and c = 70. To find the roots of the equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values, we get:
x = (-45 ± √(45² - 4(5)(70))) / (2(5))
Simplifying further gives us:
x = (-45 ± √(2025 - 1400)) / 10
And finally, calculating the square root and applying the ± gives us the two roots:
x = (-45 ± √625) / 10
x = (-45 ± 25) / 10
which can be further simplified to:
x = -7 or x = -2
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