Question

Find a quadratic polynomial whose zero are -2/under root 3 and root 3/4

Answer 1

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