JEE Advanced Model Paper 14 with solutions for online practice

f (x) = (x - a) (x - c) (x - e) + λ (x - b) (x - d)
⇒ f (a) = λ (a - b) (a - d)
⇒ f (b) = (b - a) (b - c) (b - c) < 0
f (c) = λ (c - b) (c - d)
f (d) = (d - a) (d - c) (d - e) > 0
f (c) = λ (e - b) (c - d)
If λ > 0 f (a) > 0, a root lies between b and
If λ < 0 f (c) < 0 , a root lies between e and
Always a root lies between d and b ⇒ all roots are real and distinct as exactly two can’t be real.
If λ = 0 roots are a , c and e