Question

If α×β be the roots of the equation 2x^2 -4x -3= 0 the value of α^2+ β^2 is

Answer 1

alpha × beta =c/a=-3/2
alpha+beta=-b/a

alpha+beta=-(-4)/2=2
(alpha +beta)square=(2)sq
α Sq+β sq+2 alpha ×β=4
α sq+β sq=4-2(-3/2)
α sq +β sq=4-(-3)
α sq +β sq=7

Answer 2

given, equadratic polynomial

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2x^2 - 4x - 3 = 0

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here ,a = 2 ,b = - 4 , c = - 3

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product of roots alpha × beta = c / a

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alpha × beta = - 3 / 2

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sum of roots alpha + beta = - b / a

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alpha + beta = - ( - 4 / 2 ) = 2

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alpha + beta = 2

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on squaring both sides , we get

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( alpha + beta )^2 = ( 2 )^2

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(alpha)^2+(beta)^2 + 2× aplha×beta = 4

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( alpha )^2+ (beta)^2 + 2 ( - 3/2)=4

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( alpha )^2 + ( beta )^2 - 3 = 4

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(alpha)^2 + ( beta )^2 = 7

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Answer:
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value of ( alpha )^2 + ( beta )^2 = 7
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