Maths : Equations.
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EXPLANATION.
α, β be the roots of the equation.
⇒ 2x² - 4x - 3 = 0.
As we know that,
Sum of the zeroes of the quadratic polynomial.
⇒ α + β = - b/a.
⇒ α + β = - (-4/2).
⇒ α + β = 2.
Products of the zeroes of the quadratic polynomial.
⇒ αβ = c/a.
⇒ αβ = (-3/2).
To find :
The value of : α² + β².
As we know that,
Formula of :
⇒ (x² + y²) = (x + y)² - 2xy.
Using this formula in the equation, we get.
⇒ α² + β² = (α + β)² - 2αβ.
Put the values in the equation, we get.
⇒ α² + β² = (2)² - 2(-3/2).
⇒ α² + β² = 4 + 3.
⇒ α² + β² = 7.
Option [B] is correct answer.
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.
Answered by
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Step-by-step explanation:
given :
- If alpha & beta be the roots of the equation 2x2−4x−3=0 , the value of α2+β2
to find :
- 2x2−4x−3=0 , the value of α2+β2
solution :
- Sum of roots = p + q = -b/a
- Product of roots = p * q = c/a
- In the given equation,
- p+q=-(-4)/2 = 2
- p* q = -3/2
- p² +q² = [p² + q² + 2pq] — 2pq = (p+q)² - - 2pq (2)² – 2 * (-3/2) = 4+3 = 7
answer :
- the answer 7
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