Question

Find the quadratic polynomial, sum and product of whose zeros are - and - 20 respectively. also find the zeros of the polynomial so obtained.

Answer 1

step by step explanation

Answer 2

Answer:

Required Quadratic Polynomial is k ( x² + x - 20 ) and Zeroes are -5 and 4.

Step-by-step explanation:

Given:

Sum of zeroes = -1

Product of zeroes = -20

To find: Quadratic polynomial and zeroes of the Quadratic Polynomial.

If α and β are zeroes of the Quadratic polynomial, then the quadratic polynomial is k ( x² - ( α + β )x + αβ )

Here, α + β = -1  and  αβ = -20

The Required Quadratic Polynomial = k ( x² - (-1)x + (-20) ) = k ( x² + x - 20 )

To find zeroes we put polynomial equal to 0.

So,

k ( x² + x - 20 ) = 0

x² + x - 20 = 0

x² + 5x - 4x - 20 = 0

x( x + 5 ) - 4( x + 5 ) = 0

( x + 5 )( x - 4 ) = 0

⇒ x + 5 = 0   and x - 4 = 0

⇒ x = -5  and x = 4

Therefore, Required Quadratic Polynomial is k ( x² + x - 20 ) and Zeroes are -5 and 4.