Question

find the quadratic polynomial whose zeroes are -2/✓3 and ✓3/4

Answer 1

quadratic polynomial is
(x+2/√3)(x-√3/4)

Answer 2

hello users. ......

solution:-
we know that;
for a quadratic equation
ax² + bx +c = 0

α + ß = -b / a
and
αß = c/a
where, α and ß are the roots of equation.

here,
α = -2/√3
and
ß = √3/4

now,
α + ß = -b/a
=> -2/√3 + √3/4 = -b/a

=> (-8+3)/4√3 = -b/a

=> -5/ 4√3 = -b/a

=> 5 / 4√3 = b /a

here,
b = 5 and a = 4√3

And
αß = c/a
=> -2/√3 × √3/4 = c/a

=> -2√3 / 4√3 = c/a

here,
c = -2√3 and a = 4√3


Hence;
required quadratic equation is
ax² + bx + c = 0

=> 4√3 x² + 5x + (-2√3) = 0

= 4√3 x² +5x - 2√3 = 0 answer

✡ hope it helps ✡