Find the quadratic polynomial, the sum of whose zeros is 0 and their product is -1. Hence, find the zeros of the polynomial.

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1. [tex] \tt{\huge{\pink{Hello!!! }}}[/tex]

   Question :

   Find the quadratic polynomial the sum of whose zeros is 0 and their product is -1 hence, find the zeros of the polynomial.

   Solution :

   [tex]\tt{\red{Given \: – }}[/tex]

   Sum of Zeroes = 0

   Product of Zeroes = -1

   A Quadratic Polynomial can be expressed as :

   [tex]\tt{ \purple{ \implies{ {x}^{2} – (sum \: of \: zeroes) + (product \: of \: zeroes) }}}[/tex]

   Hence The required Polynomial becomes :

   [tex]\tt{ \orange{ \implies{ {x}^{2} – 0x – 1 = > {x}^{2} – 1}}}[/tex]

   Factoring The Above Expression :

   [tex]\tt{\green{\implies{ (x-1)(x+1) }}}[/tex]

   The Required Zeroes are 1 and -1.

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2. Answer:

   Let the zeroes be α and β

   Given α + β = 0

   αβ = -1

   The quadratic polynomial is x² – Sx + P

   where S = α + β

   and P = αβ

   The polynomial is x² – (0)x + (-1)

   or x² -1

   The zeroes of this polynomial can be found by equating the expression to 0.

   x² – 1 = 0

   or x² = 1

   or x = ±1

   Do mark as brainliest if it helped!

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