Question

Write a quadratic equation with roots of 3/4 and -4

Answer 1

A quadratic equation given roots is solved by using the relation

${x}^{2} - (sum \: of \: roots)x + product \: of \: roots$

from the question,

sum of the root will be

$\frac{3}{4} + ( - 4) = \frac{3}{4} - 4$

$= \frac{3 - 16}{4}$

$= \frac{ - 13}{4}$

and also, product of the roots will

be

$\frac{3}{4} \times ( - 4) = - 3$

now substituting the sum of roots and product of roots into the equation

${x}^{2} - ( - \frac{13}{4} )x - 3$

$= {x}^{2} + \frac{13}{4} x - 3$

as the quadratic equation for the root 3/4 and -4