Question

Find quadratic polynomial whose zeros are -4/5 & 1/2

Answer 1

Answer:  10X^2+3X-4=0

Step-by-step explanation:

GIVEN',  

ZEROES OF POLYNOMIAL ARE -- ALPHA=-4/5,BHETA =1/2

ACORRDING TO PROBLEM,

ALPHA+BHETA=-4/5+1\2= -3/10

ALPHA*BHETA= -4/5*1/2= -2/5

QUADRATIC EQUATION'

x^2- (alpha+bheta)x+alphabheta=0

substIuting values,

x^2-(-3/10)x+(-2/5)=0

after simplifying we get

10x^2+3x-4=0.........

this is done.........                                         (^ refers to square)

Answer 2

The zeroes are:

$\alpha= \frac{-4}{5} \:and\: \beta  = \frac{1}{2}\\\\Quadratic \: Polynomial\\=x^{2} -(\alpha +\beta )x+\alpha \beta \\ =x^{2} - \bigg( \frac{-4}{5}+ \frac{1}{2} \bigg)x+ \bigg( \frac{-4}{5}  \bigg) \bigg( \frac{1}{2} \bigg)\\=x^{2} - \bigg( \frac{-8+5}{10} \bigg)x- \frac{4}{10}\\=x^{2} + \frac{3}{10}x- \frac{4}{10}\\=<u><em><strong>10x^{2} +3x+4</strong></em></u>$