X^4-5001X^2+6247500 Find the value of X.
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Answer:
Since it is given that the quadratic equation x
2
−(p+2)x+4=0 has equal roots, therefore, b
2
−4ac=0 where a=1,b=(p+2) and c=4:
b
2
−4ac=0
⇒(p+2)
2
−(4×1×4)=0
⇒[p
2
+2
2
+(2×p×2)]−16=0(∵(a+b)
2
=a
2
+b
2
+2ab)
⇒p
2
+4+4p−16=0
⇒p
2
+4p−12=0
⇒p
2
+6p−2p−12=0
⇒p(p+6)−2(p+6)=0
⇒(p−2)(p+6)=0
⇒p−2=0,p+6=0
⇒p=2,p=−6
Hence, p=2,−6.
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