the equation x+ root 2 =0 has
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Answer:
The discriminant of a quadratic equation
ax
2
+bx+c=0 is given by b
2
−4ac
a=2,b=2(p+1) and c=p
[2(p+1)]
2
−4(2p)⇒4(p+1)
2
−8p
⇒4[(p+1)
2
−2p]⇒4[(p
2
+2p+1)−2p]
⇒4(p
2
+1)
For any real value of p,4(p
2
+1) will always be positive as p
2
cannot be negative for real p.
Hence, the discriminant b
2
−4ac will always be positive.
When the discriminant is greater than 0 or is positive, then the roots of a quadratic equation will be real.
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