Question

If a and b are zeros of 7x2+20x-5 then value of 1/a+1/b is

Answer 1

ANSWER

The value of 1/a + 1/b is 4

GIVEN

The quadratic polynomial is

• 7x² + 20x - 5
• a and b are the zeroes of the polynomial

TO FIND

• The value 1/a + 1/b

CONCEPT TO BE USED

In a quadratic polynomial :

$\tt \star \: \: sum \: of \: the \: zeroes = - \dfrac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$

$\tt \star \: \: product \: of \: the \: zeroes = \dfrac{constant \: term}{coefficient \: of \: {x}^{2} }$

SOLUTION

We are given the polynomial ,

➜ 7x² + 20x - 5

Now from the relationships of the zeroes of the polynomial we have ,

From sum of the zeroes ,

$\sf \implies a + b = -\dfrac{20}{7} \longrightarrow (1)$

Again , from product of the zeroes

$\sf \implies ab = \dfrac{-5}{7} \longrightarrow(2)$

Dividing (1) by (2) we have,

$\sf\implies \dfrac{a + b}{ab} = \dfrac{-\dfrac{20}{7}}{\dfrac{-5}{7}}\\\\ \sf\implies \dfrac{a}{ab}+\dfrac{b}{ab} =\dfrac{20}{7}\times \dfrac{7}{5} \\\\ \sf\implies \dfrac{1}{b}+\dfrac{1}{a}=4 \\\\ \sf \implies \dfrac{1}{a}+\dfrac{1}{b}=4$