Question

if alpha and beta are the zeros of the polynomial X whole square - 8 x + 15 then find the values of of one by Alpha Plus One by beta without finding the zeros​

Answer 1

ANSWER:

• The value of the above expression is 8/15

GIVEN:

$x {}^{2} - 8x + 15$

TO FIND:

$\frac{1}{ \alpha} + \frac{1}{ \beta}$

SOLUTION:

$x {}^{2} - 8x + 15 \\ \alpha \: + \beta \: = \frac{ - (coefficient \: of \: x)}{coefficient \: of \: x {}^{2} } \\ \alpha \: + \beta \: = \frac{8}{1} \\ \\ \alpha \: \times \beta \: = \: \frac{costant \: term}{(coefficient \: of \: x {}^{2}) } \\ \alpha \: \times \beta = \frac{15}{1}$

Now finding the value of the above expression:

$= \frac{1}{ \alpha} + \frac{1}{ \beta} \\ = \frac{ \alpha \: + \beta}{ \alpha \times \beta} \\ = \frac{ \alpha \: + \beta}{ \alpha \beta} \\ putting \: the \: values \\ = \frac{8}{15}$

NOTE:

some important formulas

• x^2 + y^2 = (x+y)^2 -2xy
• (x+y)^2 = (x-y)^2 + 4xy
• (x-y)^2 = (x+y)^2 - 4xy
• x^2 + y^2 = (x-y)^2 +2xy

Answer 2

Answer:

Given:

Alpha and beta are the zeros of the polynomial x^2 - 8 x + 15.

To Find:

We need to find the values of 1/α + 1/β.

Solution:

Given polynomial is x^2 - 8 x + 15.

Sum of zeroes = α + β = -b/a = -(-8) /1 = 8

Product of zeroes = αβ = c/a = 15/1 = 15

Now we need to find the value of 1/α + 1/β.

1/α + 1/β

= (α + β)/αβ

We have α + β = 8 and αβ = 15.

Substituting the values, we get

1/α + 1/β

= (8)/15

Hence the value of 1/α + 1/β is 8/15.