Question

Find the polynomial whose zeroes are ¼ and -¼.​

Answer 1

Answer:

1/4X^2+3/4y+0=0 please like it

Answer 2

${\huge{\underline{\underline{\sf{\blue{SOLUTION:-}}}}}}$

$\underline{\sf{\green{Question}}}$

⠀⠀⠀⠀⠀• Find the polynomial whose zeroes are ⠀⠀⠀⠀⠀¼ and -¼.

$\underline{\sf{\green{Answer}}}$

⠀⠀⠀⠀⠀• Polynomial is 16x²-0x-1

$\underline{\sf{\green{Given}}}$

⠀⠀⠀⠀⠀• Zeros 1/4 and -1/4

$\underline{\sf{\green{To \: Calculate}}}$

⠀⠀⠀⠀⠀• Polynomial

$\underline{\sf{\green{Explanation}}}$

Zeros are 1/4 and -1/4 ( $\underline{\sf{\red{Given}}}$ )

Let α= 1/4

and β = -1/4

$\underline{\sf{\blue{Sum\: of \: Zeros ⟹ α+β}}}$

⟹ 1/4+(-1/4)

⟹ 1/4-1/4

⟹ 1-1 /4

⟹ 0/4

⟹ 0

$\underline{\sf{\blue{Product\:of \: Zeros⟹ αβ}}}$

⟹ 1/4×(-1/4)

⟹ -1/16

For Find Polynomial ⤵️

${\boxed{\red{\tt{x²-(α+β)x+ αβ }}}}$

Putting values,

⟹ x²- (0)x +-1/16 =0

⟹ x²-0x -1/16 =0

⟹ 16x²-0x -1=0

${\huge{\underline{\underline{\sf{\blue{Hence}}}}}}$

⠀⠀⠀⠀⠀• Polynomial is 16x²-0x-1

____________________________________________

⠀⠀⠀⠀⠀${\boxed{\red{\tt{Additional \: Information}}}}$

1) If α,β,γ are the zeros of p(x) = ax³+bx²+cx+d

Then

i) ( α+β+γ) = -b/a

ii) ( αβ+βγ+γα ) = c/a

iii) αβγ = -d/a

2) A Cubic polynomial whose zeros are α,β, γ is Given by

p(x) = { x³-(α+β+γ)x²+(αβ+βγ+γα)x-αβγ}

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