Question

find quadratic equation whose roots are 2/3 and -1/2

Answer 1

Roots of the Quadratic equation are 2/3 and -1/2
so 
equation is (x-a)(x-b)=0
where a,b are the roots of the quadratic equation

Similarly, (x-2/3)(x-(-1/2))=0
(x-2/3)(x+1/2)=0
Solving this , You will get
x^2-x/6-1/3=0
further solving 
6x^2-x-2=0

Answer 2

We know that quadratic equation is of the form

${x}^{2} - (sum \: of \: zeroes)x + product \: of \: them$
Now we know applying this formula in thia
${x}^{2} - (2 \div 3 - 1 \div 2)x + 2 \div 3 \times - 1 \div 2$
So we get have got
${x}^{2} - (1 \div 6)x - 1 \div 3$

This is your answer