Question

, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization 8/4 and 4/3​

Answer 1

Step-by-step explanation:

Let a and b be the two zeroes of the quadratic polynomial.

Given:

1. a+b=8/4=2.
2. ab=4/3.

To find: Quadratic polynomial and its roots by factorisation method.

Formula of quadratic polynomial:

${x}^{2} - (a + b)x + ab$

By substituting the given in formula:

$= > {x}^{2} - 2x + \frac{4}{3}$

$= > \frac{3 {x}^{2} - 6x + 4 }{3} = 0$

The required quadratic equation is:

3x²-6x+4=0

Answer 2

$\huge \sf \underline\red {Solution:}$

A quadratic polynomial formed for the given sum and product of zeros is given by:

f(x) = x2 + -(sum of zeros) x + (product of roots)

Here, the sum of zeros is = -8/3 and product of zero= 4/3

Thus,

The required polynomial f(x) is,

⇒ x

2

- (-8/3)x + (4/3)

⇒ x

2 + 8/3x + (4/3)

So, to find the zeros we put f(x) = 0

⇒ x

2 + 8/3x + (4/3) = 0

⇒ 3x2 + 8x + 4 = 0

⇒ 3x2 + 6x + 2x + 4 = 0

⇒ 3x(x + 2) + 2(x + 2) = 0

⇒ (x + 2) (3x + 2) = 0

⇒ (x + 2) = 0 and, or (3x + 2) = 0

Therefore, the two zeros are -2 and -2/3.