Question

form equation whose roots are 2/3 and 3/4​

Answer 1

Answer:

Sum of zeroes = 3/4 -2/3

= (9-8)/12

=1/12

Product of zeroes = 3/4 × -2/3

= -6/12 = -1/2

Quadratic eq is

x^2 -(sum of zeroes)x + product of zeroes

= x^2 - x/12 -1/2

=12x^2 - x -6

Step-by-step explanation:

Answer 2

Answer:

$12x^{2} -17x+6=0$ is the equation.

Step-by-step explanation:

$ax^{2} +bx+c=0$ is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Sum of two roots = $\frac{2}{3}+\frac{3}{4}= \frac{8+9}{12} = \frac{17}{12}$

Multiplication of two roots = $\frac{2}{3} * \frac{3}{4} = \frac{1}{2}$

New equation is

$x^{2} - \frac{17}{12}x+\frac{1}{2} =0$

⇒ $12x^{2} -17x+6=0$.

#SPJ2