Question

the quadratic equation with roots 1 by 2 and 1 by 3 is​

Answer 1

Answer:

Roots are - 1 and - 2

Sum of roots = - 1 - 2 = -3

Product of roots = (-1)(-2) = 2

Required equation is

x^2 - (sum of roots) x + Product of roots = 0

=> x^2 - (-3)x +2 = 0

=> x^2 +3x +2 = 0

This is the required equation

Answer 2

Hey dude here is your answer:----

The sum of the zeros= -b / a

$\alpha + \beta = \frac{ - b}{a}$

$\alpha + \beta = \frac{</u></em></strong><strong><em><u>-</u></em></strong><strong><em><u>1}{2} = - \frac{ - b}{a} \\ \\ and \:$

Product of the zeros = c/a

$\alpha \times \beta = \frac{c}{a} \\ \\ \alpha \beta = \frac{1}{3}$

By multiplying 3 in denominator of 1st zeroes of the polynomial and 2 in 2nd , we get ......

$a = 6 \\ \\ b = - 1 \\ and \\ \\ c = 1$

The required quadratic polynomial is ;

ax²+bx+c= 0

$6 {x}^{2} + ( - 1)x + 1 = 0 \\ \\ 6 {x}^{2} - x + 1 = 0$

✌️I hope it will be correct .......✌️