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 1

*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,

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