Question

if alpha and beta are the zeros of the polynomial 2 X square + 3 X + 5 then find 1/alpha and 1/beta​

Answer 1

Given that :

α and β are the zeros of the polynomial p(x) = 2x² + 3x + 5.

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To find :

The value of 1/α+ 1/β

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Solution :

We know,

Sum of the zeros of a quadratic polynomial(ax² + bx + c) is

$\sf \: \alpha + \beta= \frac{-coefficient \: of \: x}{coefficient \: of \: x²} = \frac{ - b}{a}$

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Product of the zeros of a quadratic polynomial(ax² + bx + c) is

$\sf \: αβ= \frac{constant \: term}{coefficient \: of \: x² } = \frac{c}{a}$

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Now,

given polynomial is 2x² + 3x + 5.

• α + β = -b/a = -3/2
• αβ = c/a 5/2

Calculating 1/α+ 1/β:

= 1/α + 1/β

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(Taking LCM)

= (α + β )/αβ

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(Putting the known values)

$\sf \: = \frac{ - 3}{2} \div \frac{5}{2} \\\\\\\sf \: = \frac{ - 3}{2} \times \frac{2}{5} \\\\\\ \sf= \frac{ - 3}{5}$