Question

Find the quadratic polynomial whose one of the zeroes is root 3/4 and product of zeroes is - 1/2

Answer 1

Answer:

let two roots be alpha and beta

so let

$\alpha = \frac{ \sqrt{3} }{4}$

so let

$\beta = x$

by the given condition

$\alpha \times \beta = - \frac{1}{2}$

so

$\alpha x = - \frac{1}{2}$

so

$x = - \frac{1}{2} \times \frac{4}{ \sqrt{3} }$

so

$x = - \frac{2 \sqrt{3} }{3}$

now

$\alpha + \beta = \frac{ \sqrt{3} }{4} - \frac{2 \sqrt{3} }{3 } = \frac{5 \sqrt{3} }{12}$

now you have alpha plus beta and aplha into beta so put the value in the equation you will get

${x}^{2} - (\frac{5 \sqrt{3} }{12} )x - \frac{1}{2 } = 0$

Answer 2

HERE IS UR ANSWER DEAR,

product of zeros = (3/4)(x) = -1/2

x = -1/2 ( 4/3)

x= -2/3

sum of zeros = -1/2 + (-2/3) = -3-2/6= -5/6

quadratic polynomial form is

= x² -( sum of zeros )x+ products of zeros

= x²- (-5/6)x -1/2