Question

If alpha and beta are the zeroes of the x²-x-4, then find out the value of one upon alpha plus one upon beta minus alpha multiply by beta​

Answer 1

Answer:

Answer:

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

α

1

+

β

1

−αβ=

4

15

Explanation:

It is given that,

\alpha \: and \betaαandβ

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}α+β=

1

−(−1)

= 11 ----(1)

ii ) Product of the zeroes = c/a

\implies \alpha \times \beta = \frac{(-4)}{1}⟹α×β=

1

(−4)

= -4−4 ----(2)

Now ,

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

α

1

+

β

1

−αβ

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

αβ

(α+β)

−αβ

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

(−4)

1

−(−4)

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

4

(−1)

+4

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

4

(−1+16)

=\frac{15}{4}

4

15

Therefore,

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

α

1

+

β

1

−αβ=

4

15