Question

Find the roots of the quadratic equations by applying the quadratic formula 1).2x²+x-4=0
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Answer 1

Answer:

Step-by-step explanation:

2x2+x−4=0

⇒ 4x2+2x−8=0 [multiplying both sides by 2]

⇒ 4x2+2x=8

⇒ (2x)2+2×2x×12+(12)2=8+(12)2

[adding (12)2 on both sides]

⇒ (2x+12)2=(8+14)=334=(33−−√2)2

⇒ 2x+12=±(33−−√2) [taking square root on both sides]

⇒ 2x+12=33−−√2 or 2x+12=−sqer(33)2

⇒ 2x=(33−−√2−12)=(33−−√−1)2

or 2x=−33−−√2−12=−(33−−√+1)2

⇒ x=(33−−√−1)4 or x=−(33−−√+1)4.

Hence, −1+33−−√4 and −1−33−−√4 are the roots of the given equation.

Answer 2

Answer:

Alpha= -1+4√2/4 and Beta= -1-4√2/4