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
Answers
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