determine the value of P for which the equation 2×^2+4 root +3+p=0 has equal roots
Answers
Answer:
ANSWER
We know that while finding the root of a quadratic equation ax
2
+bx+c=0 by quadratic formula x=
2a
−b±
b
2
−4ac
,
if b
2
−4ac>0, then the roots are real and distinct
if b
2
−4ac=0, then the roots are real and equal and
if b
2
−4ac<0, then the roots are imaginary.
Here, the given quadratic equation (3p+1)c
2
+2(p+1)c+p=0 is in the form ax
2
+bx+c=0 where a=(3p+1),b=2(p+1)=(2p+2) and c=p.
It is given that the roots are equal, therefore b
2
−4ac=0 that is:
b
2
−4ac=0
⇒(2p+2)
2
−(4×(3p+1)×p)=0
⇒(2p)
2
+2
2
+(2×2p×2)−4(3p
2
+p)=0
⇒(4p
2
+4+8p)−12p
2
−4p=0
⇒4p
2
+4+8p−12p
2
−4p=0
⇒−8p
2
+4p+4=0
⇒−4(2p
2
−p−1)=0
⇒2p
2
−p−1=0
⇒2p
2
−2p+p−1=0
⇒2p(p−1)+1(p−1)=0
⇒(2p+1)=0,(p−1)=0
⇒2p=−1,p=1
⇒p=−
2
1
,p=1
Hence, p=−
2
1
brilliant answer do
or p=1
Answer:
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