Question

Find the zeros of polynomial f(a)=4√3a²+5a-2√3 and verify the relationship between the zero and its coefficient

Answer 1

Hii friend,

F(A) = 4✓3A²+5A-2✓3

=> 4✓3A² +8A-3A-2✓3

=> 4A(✓3A+2) -✓3(✓3A+2)

=> (✓3A+2)(4A-✓3)

=> (✓3A+2) = 0 OR (4A-✓3) = 0

=> A = -2/✓3 OR A = ✓3/4

Let Alpha = -2/✓3 and Beta = ✓3/4


Relationship between the zeros and the coefficient.


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


And,

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


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