Question

Find a quadratic polynomial the product and the sum of whose zeros are -6 and 2/3

Answer 1

Heya !!

Here is your answer.

Given :-
Sum of zeroes = 2/3
Product of zeroes = -6

A Quadratic Equation is of the form :
p (x) = kx² - (Sum of zeroes)x + Product Of Zeroes
= x² - (2/3)x + (-6)
= x² - 2/3 × x - 6

Multiplying whole equation by 3.. we get
p (x) = 3x² - 2x - 18

Hope You Got It

Answer 2

HELLO DEAR,

GIVEN that:-

$\alpha \beta = - 6 \\ \\ \: \: \: \: \: \: and \\ \\ \alpha + \beta = \frac{2}{3}$


we know the:-


quadratic formula


${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ = > {x}^{2} - \frac{2}{3} x + ( - 6) = 0 \\ \\ = > 3 {x}^{2} - 2x - 18 = 0$


I HOPE ITS HELP YOU DEAR,
THANKS