find the qadratic polynomial with zeroes 2and-1 by 3
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Step-by-step explanation:
The equation will be
x²−(-1/3+2)x+(2)(−1)=0
=x²−5/3x−2
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Answer:
The zeroes of the polynomial are 2 and -1/3
Sum of the zeroes = 2 + -1/3
= 2 - 1/3 = 6 - 1/3 = 5/3
i. e., alpha + beta = 5/3
Product of zeroes = 2 × -1/3
= -2/3
i. e., alpha × beta = -2/3
Then the polynomial is of the form,
x² - (alpha + beta) × x + (alpha × beta ) = 0
x² - 5/3 × x + -2/3 = 0
x² - 5x/3 - 2/3 = 0
3x² - 5x - 2/3 = 0
3x² - 5x - 2 = 0
So the polynomial is
3x² - 5x - 2
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