Question

find a quadratic polynomial whose zeroes are 2√3 and −5√3

Answer 1

Hi ,

Let m , n are two zeroes of the quadratic

polynomial .


m = 2√3 , n = - 5√3 ,

i ) m + n = 2√3 - 5√3 = - 3√3

ii ) mn = ( 2√3 )( -5√3 ) = - 30

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Form of a quadratic polynomial whose

zeroes are m , n

x² - ( m + n )x + mn

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Therefore ,

Required polynomial is ,

p( x ) = x² - ( - 3√3 )x + ( - 30 )

= x² + 3√3x - 30

I hope this helps you.

: )

Answer 2

Hii friend,

Let Alpha = 2✓3 and Beta = -5✓3

Sum of zeros = (Alpha + Beta) = {2✓3+(-5✓3)} => 2✓3 -5✓3 = -3✓3

And,

Product of zeros = (Alpha × Beta) = (2✓3×(-5✓3) = 2×-5 × 3 = -30

Therefore,

Required polynomial = X²-(Alpha + beta)X+ Alpha × Beta

=> X²-(3✓3)X +(-30)

=> X²-(-3✓3X)-30.

=> X²+3✓3X-30.

HOPE IT WILL HELP YOU..... :-)