what numbers have a product of 9/16 and a sum of -3/2?

Question

undeadknight26 · Answer

Are there choices?

anonymous · Answer

no

undeadknight26 · Answer

@SolomonZelman

solomonzelman · Answer

$\Large\color{blue}{ \sf     a \times b=9/16 }$
$\Large\color{blue}{ \sf     a + b=-3/2 }$

if this is because you need to solve a quadratic equation, then use a quadratic formula instead, don't factor (unless you really have to)

solomonzelman · Answer

can you solve for a and b ?  (doesn't matter which one is which)

anonymous · Answer

i dont understand

solomonzelman · Answer

You don't why I wrote what I wrote in blue ?

anonymous · Answer

well i mean its just that, how do u solve for a and b and there isnt two integers

solomonzelman · Answer

$\Huge\color{blue}{ \sf     \frac{9}{16} =a \times b}$

$\Huge\color{blue}{ \sf     -\frac{3}{2} =a + b}$


red is the equation that results after I divide the first blue equation by b on both sides.$\Huge\color{red}{ \sf     \frac{9}{16b} =a }$

solomonzelman · Answer

I got disconnected...

solomonzelman · Answer

Substitute the left side of the red equation above, for a.

$\Huge\color{red}{ \sf    -\frac{3}{2}=  \frac{9}{16b}+b }$



$\Huge\color{red}{ \sf    -\frac{3}{2}=  \frac{9}{16b}+\frac{16b^2}{16b} }$


$\Huge\color{red}{ \sf    -\frac{3}{2}= \frac{9+16b^2}{16b} }$

solomonzelman · Answer

Cross multiply.

$\Huge\color{red}{ \sf    -\frac{3}{2}= \frac{9+16b^2}{16b} }$

$\Huge\color{red}{ \sf    \frac{-3}{2}= \frac{9+16b^2}{16b} }$

$\Huge\color{red}{ \sf    -48b=18+36b^2}$

solomonzelman · Answer

$\Huge\color{red}{ \sf    -48b=18+36b^2}$


$\Huge\color{red}{ \sf    36b^2-48b+18=0}$


$\Huge\color{red}{ \sf    18b^2-24b+9=0}$

can you solve this quadratic ?

anonymous · Answer

the answer is 3/4

anonymous · Answer

thats what the book told me but i dont know how they got it