Question

Let a, ß are the roots of the quadratic equation 2x² – mx –8 = 0. If m, and m, are the two values of
m for which la-Bl=m-1, then (m, + m2) is equal to :
(1) 3
(2) 8/3
(3)-3/8
(4) -8​

Answer 1

Answer:

option is B 8/3

Step-by-step explanation:

2x

2

−mx−8=0

Let α,β be the roots of the above equation.

So, α+β=m/2,αβ=−4

(α+β)

2

=α

2

+β

2

+2βα

m

2

/4=α

2

+β

2

−8

α

2

+β

2

=m

2

/4+8

(α−β)

2

=α

2

+β

2

−2βα

(α−β)

2

=m

2

/4+8+8=m

2

/4+16

α−β=

4

m

2

+64

=

2

m

2

+64

Given |α−β |=m−1.

So,

2

m

2

+64

=m−1

m

2

+64

=2m−2

Squaring on both sides,

m

2+64=4m

2 +4−8m

3m

2 −8m−60=0

3m

2-18m+10m−60=0

3m(m−6)+10(m−6)=0

(3m+10)(m−6)=0

m=6,−10/3

So, m is 6, -10/3.

The sum of both values of m are 8/3.

Hence option B.