UPSEE 2019 Solved Paper

Some error in question4k2−(5k+1)x+5k=0

let α, β be roots
then α-β = 1

we know In a standard Quadratic Equation ax2+bx+c=0
then sum of roots =−

b

a

products of roots =

c

a

Similarly
α+β=

5k+1

4

αβ=

5k

4

⇒|α=β|=1
⇒(α−β)2=1
⇒ α2+β2−2αβ=1
⇒(α+β)2−4αβ=1
(‌

5k+1

4

)2−4×‌

5k

4

=1
‌

(5k+1)2

16

−‌

20k

4

=1
25k2+1+10k−80k−16=0
25k2−70k−15=0
(5k+1)(k−3)=0
Possible values of k=3,k=−

1

5

sum=3+(−

1

5

)=

14

5