AP EAMCET Engineering 18 Sep 2020 Shift 2 Paper

Let α be the common root of given Equations
⇒‌‌α2−8α+7=0...(i)
α2−2aα+49=0.....(ii)
From Eq (i) - Eq.(ii)
⇒‌‌(−8+2a)α−42=0
2(−4+a)α=42
α=‌

21

a−4

On putting value of α in Eq. (i),
(‌

21

a−4

)2−8(‌

21

a−4

)+7=0
441−168(a−4)+7(a−4)2=0
7a2−224a+1225=0
Here, D>0
∴ Above quadratic equation have two distinct real roots.
∴ Number of possible value of a are 2