Question

find the quadratic polynomial whose zeroes are -5 and 6

Answer 1

heya dear here is ur ans. ☜☆☞
The quadratic polynomial is .
Sum of zeroes α+β
-5+6= 1
and product
αβ
-5×6= -30
x²-1x -30

Answer 2

The quadratic polynomial is x² - x - 30

Given :

The zeroes of a quadratic polynomial are - 5 and 6

To find :

The quadratic polynomial

Concept :

If the Sum of zeroes and Product of the zeroes of a quadratic polynomial is given then the quadratic polynomial is

$\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }$

Solution :

Step 1 of 2 :

Write down the zeroes of the quadratic polynomial

Here it is given that zeroes of a quadratic polynomial are - 5 and 6

Step 2 of 2 :

Find the quadratic polynomial

Sum of the zeroes = - 5 + 6 = 1

Product of the zeroes = - 5 × 6 = - 30

Hence the required Quadratic polynomial

$\displaystyle \sf= {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes$

$\displaystyle \sf= {x}^{2} -(1 )x + ( - 30)$

$\displaystyle \sf= {x}^{2} -x - 30$