Question

Find the values of p for which the quadratic equation x2

– px + p + 3 = 0 has

(i) coincident roots

(ii) real, distinct roots,

(iii) one positive and one negative root.​

Answer 1

Answer

Correct option is

A

One positive and one negative root.

x

2

−px+p+3=0

(a) one positive root and one negative root:

⇒ product of roots should be negative.

⇒ (P+3)<0.

⇒ P<−3

and Δ>0

P

2

−4(p−3)>0.

P

2

−4p+12>0

(P−2)

2

+8>0.

(b) both roots are negative :

⇒ sum of roots = negative

⇒ P=negative

⇒P<0

product of roots should be positive

P+3>0

P>−3

∴P∈(−3,0)