Find the polynomial whose zeroes are root3by2 and minus root 3 by 2
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Zeroes are ✓3/2 and -✓3/2
Sum of zeroes = ✓3/2 + (-✓3/2)
=> ✓3/2 - ✓3/2
=> ✓3/✓2 - ✓3/✓2
=> ✓3 - ✓3 / ✓2
=> 0/✓2 = 0
And,
Product of zeroes = ✓3/2 × -✓3/2
=> ✓3/✓2 × -✓3/✓2
=> -3/2
Therefore,
Required quadratic polynomial = X²-(Sum of zeroes )X + product of zeroes
=> X² - (0)X + (-3/2)
=> X² - 3/2
=> 2X² - 3
★ HOPE IT WILL HELP YOU
Sum of zeroes = ✓3/2 + (-✓3/2)
=> ✓3/2 - ✓3/2
=> ✓3/✓2 - ✓3/✓2
=> ✓3 - ✓3 / ✓2
=> 0/✓2 = 0
And,
Product of zeroes = ✓3/2 × -✓3/2
=> ✓3/✓2 × -✓3/✓2
=> -3/2
Therefore,
Required quadratic polynomial = X²-(Sum of zeroes )X + product of zeroes
=> X² - (0)X + (-3/2)
=> X² - 3/2
=> 2X² - 3
★ HOPE IT WILL HELP YOU
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