Question

Find a quadratic polynomial whose sum and product of zeros are given as -3/2root5and -1/2

Answer 1

Answer:

k(2x^2+3x-1)=0\:,where\:'k'\:is\:a\:constant

Step-by-step explanation:

Given:

• sum of roots =$\dfrac{-3}{2}$
• product of roots=$\dfrac{-1}{2}$

pre-requisite knowledge

• sum of roots=$\alpha +\beta =\dfrac{-b}{a}$
• product of zeros =$\alpha\times\beta =\dfrac{c}{a}$
• $x^2+(\alpha +\beta )x+(\alpha\times\beta)$

solution:

$\alpha +\beta =\dfrac{-b}{a}=\dfrac{-3}{2}\\\\\alpha\times\beta =\dfrac{c}{a}=\dfrac{-1}{2}\\\implies\:a=2\\b=3\\c=-1\\thus\:equation\:becomes=k(2x^2+3x-1)=0\:,where\:'k'\:is\:a\:constant$