Question

if alpha,beta are the zeros of polynomial p(x) = 4x^2+4x+7 then find the value of 1/alpha -1/beta

Answer 1

Given

p(x) = 4x^2+4x+7

here,

a= 4, b=4 and c= 7

→we know that ,

sum of zeroes= -b/a

$\alpha + \beta = \frac{ - 4}{4} = - 1$
—————————————(1)

also,

→ product of zeroes = c/a

$\alpha \beta = \frac{7}{4}$
—————————————(2)

now, it is given that,

$\frac{1}{ \alpha } - \frac{1}{ \beta } \\ \\ = \frac{ \beta + \alpha }{ \alpha \beta } \\ \\ = - 1 \div \frac{7}{4} \\ \\ = \frac{ - 4}{7}$