Question

Find a quadratic polynomial whose sum and product of zero is -2,1/2 respectively

Answer 1

$\huge\mathfrak{Answer:}$

Given:

• We have been given that sum of zeroes of a quadratic polynomial is 2 and product of its zeroes is 1/2.

To Find:

• We need to find the quadratic polynomial.

Solution:

We have been given the sum of zeroes of a quadratic polynomial is 2 and product of its zeroes is 1/2.

Sum of zeroes (α + β) = -2

Product of zeroes (αβ) = 1/2

Now, We can find the quadratic polynomial by this formula:

$\mapsto\sf{k[{ {x}^{2} - ( \alpha + \beta )x + \alpha \beta }]}$

Substituting the values, we have

$\longrightarrow\sf{k [{x}^{2} - ( -2 )x + ( \dfrac{1}{2})]}$

$\longrightarrow\sf{ {x}^{2} + 2x + \dfrac{1}{2}}$

Hence the required polynomial is

(x² + 2x - 1/2).