Question

One root of 2x2 - 10x +p = 0 is 2/3 find the other.

Answer 1

Let the roots of the given equation be a and b. Given a=2/3. From the given equation,a+ b=-(-10)/2 ( since,sum of the roots of a quadratic equation = -(coefficient of x)/(coefficient of x power 2)) So,2/3+b=5 b=5-2/3 b=(15-2)/3 b=13/3. And,ab=p/2(since,product of the roots of a quadratic equation=(constant term)/(coefficient of x power 2)) (2/3)(13/3)=p/2 p=(26/9)*2 p=52/9.