Question

find the zeroes of the polynomial 4✓3^2+5x-2✓3 and verify the relationship between zeroes and it's coefficients

Answer 1

Hiii friend,

P(X) => 4✓3X²+5X-2✓3

=> 4✓3X² +8X -3X - 2✓3

=> 4X(✓3X² +2) - ✓3(✓3X + 2)

=> (✓3X²+2) ( 4X-✓3)= 0

=> (✓3X+2) = 0 OR (4X - ✓3) = 0

=> X = -2/✓3 OR X = ✓3/4

Alpha = -2/✓3 and Beta = ✓3/4

Relationship between the zeros and Coefficient.

Sum of zeroes = Alpha + Beta = (-2/✓3 + ✓3/4)= (-8 + 3/4✓3 )= (-5/4✓3)= -(Coefficient of X)/(Coefficient of X²)

Product of zeroes = Alpha × Beta) = -2/✓3 × ✓3/4 = -2✓3/4✓3 = Constant term/Coefficient of X².

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