Question

if alpha and beta are the zeros of the polynomial PX= 4x^2+3x+7 then find the value of 1/alpha - 1/ beta

Answer 1

Let alpha and beta be the zeroes of p(x)=4x +3x+7

Now, In Polynomial,
a=4, b=3 and c=7

Now,
alpha+beta= -b/a= -3/4
alpha*beta= c/a=7/4

Now, According to question,

alpha^-1 +beta^-1
= (1/apha)+(1/beta)
= alpha+beta/alpha*beta --(By taking alpha*beta as LCM)
= (-3/4)/(7/4)
= -3/7
Required Answer--> -3/7