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If α,β are the roots of 4x²+7x+2=0 then the equation whose roots are α²,β² is ??????????

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by kittu1422

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by kittu1422

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So we know that for quadratic equation ax² +bx +c = 0

whose roots are m,n we know that x² - ( m + n)x +mn = 0 the previous quadratic equation

we know sum of roots = -b/a

product of roots = c/a

so in this sum

roots of the equation are 4x² +7x + 2 = 0

α +β = -7/4

αβ = 2/4 = 1/2

so to form the quadratic equation as given above using x² - ( m + n)x +mn = 0

so x² - ( α² + β² )x + (αβ)² = 0

so using formula a² +b² = (a +b)² - 2ab

so x² - ( α² + β² )x + (αβ)² = 0

⇒x² - {(α+ β)² - 2αβ }x + (αβ)² = 0

⇒x² - {(-7/2)² - 2 ×1/2}x + (1/2)² = 0

⇒4x² - 49x + 1 = 0

so the required quadratic equation is

4x² - 49x + 1 = 0

whose roots are m,n we know that x² - ( m + n)x +mn = 0 the previous quadratic equation

we know sum of roots = -b/a

product of roots = c/a

so in this sum

roots of the equation are 4x² +7x + 2 = 0

α +β = -7/4

αβ = 2/4 = 1/2

so to form the quadratic equation as given above using x² - ( m + n)x +mn = 0

so x² - ( α² + β² )x + (αβ)² = 0

so using formula a² +b² = (a +b)² - 2ab

so x² - ( α² + β² )x + (αβ)² = 0

⇒x² - {(α+ β)² - 2αβ }x + (αβ)² = 0

⇒x² - {(-7/2)² - 2 ×1/2}x + (1/2)² = 0

⇒4x² - 49x + 1 = 0

so the required quadratic equation is

4x² - 49x + 1 = 0