Question

p(x)=6x^2+x-2. if
$\alpha and \beta are \: the \: zeroes \: of \: the \: polynomialthen \: find \: \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha }$
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Answer 1

given polynomial :-

p(x) = 6x² - x - 2

here we have to find the value of alpha/beta + beta/alpha.

so first we needa find alpha and beta (zeroes of the polynomial).

using splitting the middle term method,

➡ 6x² + x - 2 = 0

➡ 6x² + (4x - 3x) - 2 = 0

➡ 6x² + 4x - 3x - 2 = 0

➡ 2x(3x + 2) + 1(3x + 2) = 0

➡ (3x + 2) (2x + 1)

• x = -2/3, = -1/2

therefore alpha is -2/3 and beta is -1/2

now, value of alpha/beta + beta/alpha = (-2/3)/(-1/2) + (-1/2)(-2/3)

= (-2/3 × -2/1) + (-1/2 × -3/2)

= 4/3 + 3/4

taking LCM of 3 and 4 = 3 × 4 = 12 we get,

= (4 × 4)/(3 × 4) + (3 × 3)/(4 × 3)

= 16/12 + 9/12

= (16 + 9)/12

= 25/12

hence, alpha/beta + beta/alpha = 25/12

Answer 2

Answer in the attachment:-