find the roots of the following quadratic equations by applying quadratic formula. ( 1) x²+4x+1=0
Please answer this it's urgent and give fully explanation
Answers
Answered by
62
Answer:
Step-by-step explanation:
Attachments:
Answered by
56
EXPLANATION.
Quadratic equation.
⇒ x² + 4x + 1 = 0.
As we know that,
⇒ D = Discriminant Or b² - 4ac.
⇒ D = (4)² - 4(1)(1).
⇒ D = 16 - 4.
⇒ D = 12.
⇒ x = - b ± √D/2a.
⇒ x = -(4) ± √12/2.
⇒ x = - 4 ± 2√3/2.
⇒ x = - 2 ± √3.
Sum of the zeroes of the quadratic polynomial.
⇒ α + β = - b/a.
⇒ α + β = - (4/1) = - 4.
Products of the zeroes of the quadratic polynomial.
⇒ αβ = c/a.
⇒ αβ = (1/1) = 1.
As we know that,
Formula of quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (- 4)x + (1) = 0.
⇒ x² + 4x + 1 = 0.
MORE INFORMATION.
Conjugate roots.
(1) If D < 0.
One roots = α + iβ.
Other roots = α - iβ.
(2) If D > 0.
One roots = α + √β.
Other roots = α - √β.
Similar questions