Question

if a and b roots of the equation 4x^2+3x++7=0 then 1/a+1/b is

Answer 1

★ AnswEr :-

$\sf\dfrac{1}{a} + \dfrac{1}{b} = - \dfrac{ 3}{7}$

★ GivEn :-

• a and b are the roots of equation 4x^2 + 3x + 7 = 0

★ To Find :-

• The value of 1/a + 1/b

Step-by-step explanation:

We know,

The formula of Quadratic equation,

$\implies \boxed{ \sf \: p {x}^{2} + qx + r = 0 \: (p \neq0)}$

$\sf \: Sum \: of \: the \: roots = - \dfrac{q}{p}$

$\therefore \sf a + b = - \dfrac{3}{4}$

And,

$\sf \: Product \: of \: roots = \dfrac{r}{p}$

$\therefore \sf \: a \times b = \dfrac{7}{4}$

Now,

$\sf \: \dfrac{1}{a} + \dfrac{1}{b}$

$: \implies \sf \: \dfrac{a + b}{ab}$

Now, putting the values,

$\implies \sf \: \dfrac{ - \dfrac{3}{4} }{ \dfrac{7}{4} }$

$\implies \sf \: - \dfrac{3}{4} \times \dfrac{4}{7}$

$\boxed{ \red{ \sf \therefore \dfrac{1}{a} + \dfrac{1}{b} = - \dfrac{ 3}{7} }}$