Question

If alpha and beta are the two zeros of polynomial x^2-3x+7 then find a quadratic polynomial of zeros 1/Alpha and 1/beta.

Answer 1

Answer:

Heya !!

X² - 3X + 7

Here,

A = 1 , B = -3 and C= 7

Sum of zeroes = -B/A

Alpha + Beta = -(-3)

Alpha + Beta = 3 --------(1)

And,

Product of zeroes = C/A

Alpha × Beta = 7 -------(2)

Zeroes of the other quadratic polynomial are 1/Alpha and 1/Beta.

Sum of zeroes of the other quadratic polynomial = 1/Alpha + 1/Beta = Beta + Alpha / Alpha × Beta

=> 3/7

And,

Product of zeroes = 1/Alpha × 1/Beta = 1/Alpha × Beta = 1/7

Therefore,

Required quadratic polynomial = X²-(Sum of zeroes)X + Product of zeroes

=> X² - (3/7)X + 1/7

=> X² - 3X/7 + 1/7

=> 7X² - 3X + 1.

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Answer 2

$\huge\pink{ANSWER}$

Therefore,

Required quadratic polynomial is...

→ x² - (Sum of zeroes) x + Product of zeroes

→ x² - ($\frac{3}{7}$) x + $\frac{1}{7}$

→ x² - $\frac{3x}{7}$ + $\frac{1}{7}$

→ 7x² - 3x + 1

Hope it helps..⭐⭐

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