If two zeroes of polynomial P(x) = 2x4+ 10x3 + 5x2 - 35x - 42 are 3and -2. Find other zeroes.
Answers
there is mistake in data , ±√7/2 are other zeroes after correction
Step-by-step explanation:
P(x) = 2x⁴ + 10x³ + 5x² - 35x - 42
3 & - 2 are zeroes
=> (x - 3) & (x + 2) are factors
=> (x - 3)(x + 2) = x² - x - 6 is a factor
2x² + 12x + 19
x² - x - 6 _| 2x⁴ + 10x³ + 5x² - 35x - 42 |_
2x⁴ - 2x³ - 12x²
_______________________
12x³ + 17x² - 35x - 42
12x³ - 12x² - 72x
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19x² + 37x - 42
19x² -19x - 114
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56x + 72
Not completely divisible
Hence there is mistake in data
P(3) also not equal to zero
but
P(-3) = 0
hence -3 & -2 are zeroes
=> (x + 3) & (x + 2) are factors
=> (x - 3)(x + 2) = x² + 5x + 6 is a factor
2x² - 7
x² +5 x + 6 _| 2x⁴ + 10x³ + 5x² - 35x - 42 |_
2x⁴ + 10 x³ + 12x²
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- 7x² - 35x - 42
- 7x² - 35x - 42
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0
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2x² - 7 = 0
=> x² = 7/2
=> x = ±√7/2
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