Question

How to find quadratic equation from sum and product of roots are given?

Answer 1

if in the question the sum of and t NBC product of the quadratic equation is given by the formula of quadratic equation we can find the equation

now quadratic formula is
= x^2 - (α + β ) x + αβ
in this we Need to substitute the sum value in the alpha + beta and the product of zeros value in the place on f alphabeta

Answer 2

Hi friend !!

If we are given the sum of the zeros and product of the zeros, we can form a quadratic equation in the following way :-

x² - (sum of zeros)x + (product of zeros)

if the sum and the product are as fraction , we can multiply the equation through out with a constant [ other than 0]

k{x² - (sum of zeros)x + (product of zeros)}

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example:-

find a quadratic polynomial whose sum and product of zeros are 1/2 and 3/2 respectively

ans:-

Let the zeros be α and β
given ,
sum of zeros = α + β =  1/2
product of  zeros = αβ = 3/2

we can form a quadratic polynomial :-

x² - (sum of zeros )x + (product of zeros)

x² - (1/2)x + 3/2

x²-1/2x+3/2

to make the equation look clear , we can multiply the whole equation with 2 .

2[x² - 1/2x + 3/2]

2x² - x + 3             ----> required polynomial