1.

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

Answer»

AnswEr:-

Quadratic POLYNOMIAL = x² - 1

ZEROES of polynomial = -1 & 1

\rule{200}{1}

Explanation:-

Let the zeroes of polynomial be α & β

Given:-

  • α + β = 0
  • αβ = -1

We know the standard form of a quadratic polynomial:-

\star\: \boxed{\boxed{\sf\blue{x^2 - (Sum \: of \: zeros)x + Product\: of\: zeros }}}

Here,

⇒ Polynomial = x² - (0)x + (-1)

⇒ Polynomial = x² - 0x - 1

⇒ Polynomial = x² - 1

Therefore,

\therefore\underline{\textsf{Quadratic polynomial = {\textbf{x$^2$- 1}}}}

\rule{200}{1}

We got the quadratic polynomial as x² - 1

Now we can FIND the zeros of polynomial by factorization method:-

⇒ x² - 1 = 0

[We know, a² - B² = (a + b)(a - b) ]

⇒ (x + 1)(x - 1) = 0

⇒ x = -1 or x = 1

Therefore,

\therefore\underline{\textsf{Zeros of polynomial = {\textbf{-1 \& 1 }}}}


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