Math, asked by darkgravegaming, 1 month ago

Find a quadratic polynomial,the sum of whose zeroes is 0 and their product is -4.Hence find the zeroes of the quadratic polynomial.​

Answers

Answered by Vikramjeeth
14

*QuEstion:

Find a quadratic polynomial,the sum of whose zeroes is 0 and their product is -4.Hence find the zeroes of the quadratic polynomial.

AnswEr:

→ Quadratic polynomial = x² - 4

→ Zeroes of polynomial = -4 & 4

Explanation:—

Let the zeroes of polynomial be α & β

Given:—

→ α + β = 0

→ αβ = -4

We know the standard form of a quadratic polynomial:

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

Here,

→ Polynomial = x² - (0)x + (-4)

→ Polynomial = x² - 0x - 4

→ Polynomial = x² - 4

Therefore,

\therefore\underline{\textsf{Quadratic polynomial = {\textbf{x$^2$- 4}}}}

We got the quadratic polynomial as x² - 4

Now we can find the zeros of polynomial by factorization method:

→ x² - 4 = 0

[We know, a² - b² = (a + b)(a - b) ]

→ (x + 4)(x - 4) = 0

→ x = -4 or x = 4

Therefore,

\therefore\underline{\textsf{Zeros of polynomial = {\textbf{-4 \& 4 }}}}

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