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
441−168a+672+7(a2+16−8a)=0
7a2−224a+1225=0 Here, D>0 ∴ Above quadratic equation have two distinct real roots. ∴ Number of possible value of a are 2