Question

find the quadratic polynoimal whose zeroes are -2/root3 and root3/4​

Answer 1

★$\huge\bf{\blue{\underline{Question:-}}}$

find the quadratic polynoimal whose zeroes are -2/root3 and root3/4

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★$\huge\bf{\red{\underline{Answer:-}}}$

4√3 x² +5x - 2√3 = 0 answer

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★$\huge\bf{\green{\underline{Explanation:-}}}$

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

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Answer 2

$\huge \tt \pink {answer}$

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

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