Question

If alpha and beta are zeroes of ploynomial x2-5x+6 find the value of 1/alpha+ 1/beta-2alpha beta

Answer 1

Refer the attachment.

Answer 2

Aɴꜱᴡᴇʀ

☞ Your answer is -11.16

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Gɪᴠᴇɴ

✭ α and β are the zeros of the polynomial x² - 5x + 6

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Tᴏ ꜰɪɴᴅ

➠ $\sf\dfrac{1}{\alpha} + \dfrac{1}{\beta} - 2\alpha\beta$

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Sᴛᴇᴘꜱ

We know that, the standard form of the quadratic polynomial is ax² + bx + c. Here,

◕ a = 1

◕ b = 5

◕ c = 6

☆ $\sf Sum\: of\: zeroes = \pink{\sf \dfrac{-(coefficient \: of \: x)}{coefficient \: of \: x^2}}$

➳ α + β = $\sf\dfrac{-(-5)}{1}$

➳ α + β = 5

☆ $\sf Product \:of\: zeroes = \pink{\sf \dfrac{constant \: term}{coefficient \: of \: x^2}}$

➳ αβ =$\sf\dfrac{6}{1}$

➳ αβ = 6

To find :

➢ 1/α+1/β+2αβ

➢ α+β/αβ-2αβ

➢ 5/6 - 2(6)

➢ 5 - 72/6

➢ -67/6 (or) -11.16

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