Question

If sum of the zeroes of a polynomial is 1/2 and product of zeroes is - 2/3 then the required polynomial is 
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Answer 1

$\huge\mathfrak{\red{Answer}}$

K[6x^2-3x-4]

Step-by-step explanation:

Given that:-

$sum \: of \: zeroes \: or \: \alpha + \beta = \: \frac{1}{2}$

..............(i)

And

$product \: of \: zeroes \: or \: \alpha \times \beta = \: \frac{ - 2}{3}$

................(ii)

Now,

we also know that

sum of zeroes = -b/a .....(iii)

&

product of zeroes = c/a ........(iv)

Now, taking LCM of denominators of both sides in (i) and (ii).

we get,

(i)= 3/6. and (ii)= -4/6

On comparing the new obtained values and (iii)&(iv) we get,

a=6, b= -3 and c= -4

Putting the values in the general form of polynomial ie k[ax^2+bx+c]

we get

$k ({6x}^{2} - 3x - 4)$ for some real number 'K'.