Question

if alpha and beta are the zeros of the quadratic polynomial x square - x minus 4 find the value of one upon alpha plus one upon beta minus alpha beta

Answer 1

there u go.....its right i think

Answer 2

Answer:

$\frac{1}{\alpha}+\frac{1}{\beta}-\alpha\beta =\frac{15}{4}$

Explanation:

It is given that,

$\alpha \: and \beta$

are two zeroes of Quadratic expression x²-x-4.

Compare above expression with ax²+bx+c , we get

a = 1 , b = -1 , c = -4

i ) sum of the zeroes = -b/a

$\alpha + \beta = \frac{-(-1)}{1}$

= $1$ ----(1)

ii ) Product of the zeroes = c/a

$\implies \alpha \times \beta = \frac{(-4)}{1}$

= $-4$ ----(2)

Now ,

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

= $\frac{(\alpha+\beta)}{\alpha\beta}-\alpha\beta$

= $\frac{1}{(-4)}-(-4)$

= $\frac{(-1)}{4}+4$

= $\frac{(-1+16)}{4}$

=$\frac{15}{4}$

Therefore,

$\frac{1}{\alpha}+\frac{1}{\beta}-\alpha\beta =\frac{15}{4}$

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