Question

Find the quadratic polynomial, whose zeroes are,
a) 1, 2
b) -2, -1
c) v3,0​

Answer 1

Answer:

Using this expression we can find quadratic polynomials

x^2 + x (alpha + beta) - (alpha)( beta)

a) x^2+ 3x - 2

b) x^2 - 3x + 2

c) x^2 + 3x

Answer 2

Given:

a) 1, 2

b) -2, -1

c) 3, 0​

To find: The quadratic polynomial for the given pair of zeroes.

Solution:

Let α and β be the two zeroes of a quadratic equation. Then, a quadratic equation can be represented as follows.

$x^{2} - (\alpha + \beta )x + (\alpha \beta ) = 0$

a) For the pair (1, 2), the sum is 3 and the product is 2. Hence, the quadratic polynomial is written as follows.

$x^{2} - 3x + 2 = 0$

b) For the pair (-2, -1), the sum is -3 and the product is 2. Hence, the quadratic polynomial is written as follows.

$x^{2} + 3x + 2 = 0$

c) For the pair (3, 0), the sum is 3 and the product is 0. Hence, the quadratic polynomial is written as follows.

$x^{2} - 3x = 0$

Therefore, the quadratic polynomial for the given pair of zeroes is:

a) x² - 3x + 2 = 0

b) x² + 3x + 2 = 0

c) x² - 3x = 0