Simplify completely: the quantity 10 times x to the 6th power times y to the third power plus 20 times x to the third power time
1 answer:
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Answer:
Step-by-step explanation:
1. Find the Greatest Common Factor of the numerator and denominator.
The prime factors of 35 are <u>5</u>, 7, 35
The prime factors of 60 are 2, 3, 4, <u>5</u>, 6, 10, 12, 15, 20, 30, 60
The only common factor of 35 and 60 is 5.
2. Divide the numerator and denominator by the Greatest Common Factor.
Answer:
Step-by-step explanation:
Given equation is,
x² + (p + 1)x = 5 - 2p
x² + (p + 1)x - (5 - 2p) = 0
x² + (p + 1)x + (2p - 5) = 0
Properties for the roots of a quadratic equation,
1). Quadratic equation will have two real roots, discriminant will be greater than zero. [(b² - 4ac) > 0]
2). If the equation has exactly one root, discriminant will be zero [(b² - 4ac) = 0]
3). If equation has imaginary roots, discriminant will be less than zero [(b² - 4ac) < 0].
Discriminant of the given equation =
For real roots,
p² + 2p + 1 - 8p + 20 > 0
p² - 6p + 21 > 0
For all real values of 'p', given equation will be greater than zero.