Question

If alpha and Bita are the zeros of the quadratic polynomial f(x) = 6x2+x-2, find the apha/Bita+Bita/alpha
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Answer 1

Answer:

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Answer 2

Answer:

So, the Polynomial given here is 6x² + x - 2

And the Zeroes are α and β

The standard form of quadratic equations is ax² + bx + c

Let's find the zeroes of this polynomial.

We have to find a pair of numbers whose sum is 1 and product is -12

That would be 4 and -3.

So,

6x² + 4x - 3x - 2

= 3x(2x-1) - 2(2x-1)

= (3x-2)(2x-1)

So, the zeroes are $\frac{2}{3} and \frac{1}{2}$.

So α÷β+β÷α

α÷β =  $\frac{2}{3}$÷$\frac{1}{2}$

$\frac{2}{3}$ × 2

= $\frac{4}{3}$

β÷α  = $\frac{1}{2}$ ÷ $\frac{2}{3}$

=  $\frac{1}{2}$ × $\frac{3}{2}$

= $\frac{3}{4}$

So,

$\frac{3}{4} + \frac{4}{3} = \frac{9}{12} + \frac{16}{12} = \frac{25}{12}$

∴ α÷β+β÷α = $\frac{25}{12}$

Hope it Helps,

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