NTSE Stage 2 SAT 2017 Question Paper

Let be the two quadratic equation since 1 is a common root.
Then,
⇒ a1+b1+c1=a2+b2+c2=0
⇒ b1=−(a1+c1)‌and‌b2=−(a2+c2)
Also, the discriminants of two quadratic equations are equal
Then
⇒ b12−4a1c1=b22−4a2c2
⇒ (a1−c1)2=(a2−c2)2
⇒ a1−c1=±(a2−c2)
Now, the roots of equation,
x=−

b1±√D1

2

=a1‌and‌c1 and the roots of equation 2,x=

−b2±√Δ2

2

=a1and c2
If a1=a2=1 be the common roots
Then, other roots are c1‌and‌c2
⇒c1−c2=a1−a2=0‌or‌c1+c2=a1+a2
⇒ c1=c2‌‌‌‌‌‌c1+c2=2
Hence, roots are either equal or their sum is 2.