Question

Find the quadratic polynomial sum of whose zeroes in 8 and their product is 12. Hence find the zeroes of the polynomial.

Answer 1

hope this helps you ☺☺☺☺

Answer 2

Aɴꜱᴡᴇʀ

☞ Quadratic polynomial = x² - 8x + 16

☞ Zeroes = 6 and 2

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Gɪᴠᴇɴ

➳ Sum of zeros = 8

➳ Product of zeros = 12

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Tᴏ ꜰɪɴᴅ

➤ The quadratic polynomial.

➤ The zeroes of the quadratic polynomial.

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Sᴛᴇᴘꜱ

✭ Let the zeroes of the quadratic polynomial be α and β respectively.

• According to the question,

❍ Sum of zeroes = 8

⇒ α + β = 8

❍ And, product of zeroes = 12.

⇒ αβ = 12

We know that,

The quadratic polynomial is written as,

= x² - (α + β)x + αβ

= x² - 8x + 12

Hence, the required quadratic polynomial is x² - 8x + 12.

Now, to find the zeroes of the quadratic polynomial ;

$\dashrightarrow\sf {x}^{2} - 8x + 12 = 0 \\ \\ \dashrightarrow \sf {x}^{2} - 6x - 2x + 12 = 0 \\ \\ \dashrightarrow \sf x(x - 6) - 2(x - 6) = 0 \\ \\ \dashrightarrow\sf (x - 6)(x - 2) = 0 \\ \\ \pink{\dashrightarrow\sf x = 6 \: \: or \: \: x = 2}$

Hence, the zeroes of the quadratic polynomial are 6 and 2.

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