.if p(x) = 5 -4x +2, find (a) p(0) (b) p(3) (c) p(-2) (d) p(-1)
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Step-by-step explanation:
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)
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