Question

if alpha and beta are the zeros of the polynomial FX =5x^2-7x+1 then find the value of Alpha/beta+beta/Alpha
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Answer 1

Answer:

The value of $\frac{\alpha }{\beta }+\frac{\beta }{\alpha}$ is 7.88.

Step-by-step explanation:

The roots of a quadratic equation ax² + bx + c = 0 are:

$x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }$

In this case:

a = 5$\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$b = -7

c = 1

Compute the roots as follows:

$x = \frac{ -(-7) \pm \sqrt{(-7)^2 - 4(5)(1)}}{ 2(5) }\\x = \frac{ 7 \pm \sqrt{49 - 20}}{ 10 }\\x = \frac{ 7 \pm \sqrt{29}}{ 10 }\\x = \frac{ 7 }{ 10 } \pm \frac{\sqrt{29}\, }{ 10 }\\x = 1.24, 0.16$

Compute the value of $\frac{\alpha }{\beta }+\frac{\beta }{\alpha}$ as follows:

$\frac{\alpha }{\beta }+\frac{\beta }{\alpha}=\frac{1.24}{0.16}+\frac{0.16}{1.24}=7.88$

Thus, the value of $\frac{\alpha }{\beta }+\frac{\beta }{\alpha}$ is 7.88.

Answer 2

Right question:

If α and β are the zeros of the quadratic polynomial f(x) = 5x² - 7x + 1, find the value of 1/$\alpha + 1/\beta$

Given:

$\alpha$ and $\beta$ are the zeros of the polynomial f(x) = 5x² - 7x + 1

To find:

$\alpha$/$\beta$ + $\beta$/$\alpha$

Solution:

In the equation given above,

a = 5,

b = -7, and

c = 1

$\alpha$ + $\beta$ = -b/a = -(-7)/5 = 7/5

$\alpha$$\beta$ = c/a = 1/5

Now,

1/$\alpha$ + 1/$\beta$ = $\alpha$ + $\beta$/$\alpha \beta$

= 7/5/1/5

= 7/5 × 5/1

= 7

Hope it helps you bro.

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