Question

$if \: \alpha \: and \: \beta \: are \: zeroes \: of \: p(x) = {x}^{2} + x \: - 1 \: then \: find \: \frac{1}{ \alpha } + \frac{1}{ \beta }$
class 10 CBSE
NCERT Mathematics
​

Answer 1

Answer:

Answer

α,β roots of f(x)=kx

2

+4x+4

Given α

2

+β

2

=24

We know α+β=

a

−b

=

k

−4

αβ=

a

c

=

k

4

(α+β)

2

=α

2

+β

2

+2αβ

(

k

−4

)

2

=24+2(

k

4

)

k

2

4

2

=24+2(

k

4

)

16=24k

2

+8k

2=3k

2

+k

0=3k

2

+k−2

0=3k

2

+3k−2k−2

0=3k(k+1)−2(k+1)

0=(k+1)(3k−2)

∴k=−1,

3

2

Step-by-step explanation:

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