Question

If alpha and beta are the zeroes of p(x)=5x^2-7x+2 then the sum of their reciprocals are

Answer 1

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Answer 2

Answer:

7/2

Step-by-step explanation:

Given : p(x) = 5x² - 7x + 2

By Middle Term Factorisation, we get

→ p(x) = 5x² - 5x - 2x + 2

→ p(x) = 5x(x - 1) - 2(x - 1)

→ p(x) = (5x - 2)(x - 1)

To find the zeroes, these factors should be equal to zero.

Using zero product rule, we get

→ (5x - 2) = 0 and (x - 1) = 0

→ x = 2/5 and x = 1

__________________________

Let α and β be the zeroes of the given polynomial.

∴ α = 2/5 , β = 1

_________________________

Now,

Sum of their reciprocal :

→${\sf{ {\dfrac{1}{\alpha}} + {\dfrac{1}{\beta}} }}$

Putting known values, we get

→ ${\sf{ {\dfrac{1}{ {\dfrac{2}{5}} }} + {\dfrac{1}{1}} }}$

→ ${\sf{ {\dfrac{5}{2}} + {\dfrac{1}{1}} }}$

→ ${\sf{ {\dfrac{5 + 1(2)}{2}} }}$

→ ${\sf{ {\dfrac{5 + 2}{2}} }}$

→ ${\boxed{\sf{\green{ {\dfrac{7}{2}} }}}}$