Question

The roots of $3x^2 - 4x + 15 = 0$ are the same as the roots of $x^2 + bx + c = 0,$ for some constants $b$ and $c.$ Find the ordered pair $(b,c).$

Answer 1

we are given

quadratic equation as

$3x^2-4x+15=0$

now, we can find b and c from

$x^2+bx+c=0$

we can see that coefficient of x^2 is 1

so, we will have to make coefficient x^2 as 1

so, we divide both sides by 3

$3x^2-4x+15=0$

$\frac{3x^2-4x+15}{3}= \frac{0}{3}$

$\frac{3x^2}{3}-\frac{4x}{3}+\frac{15}{3}= \frac{0}{3}$

now, we can simplify it

$x^2-\frac{4}{3}x+5= 0$

now, we can compare it with

$x^2+bx+c=0$

we get

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

$c=5$

so, we get order pair as

$(b,c)=(-\frac{4}{3} , 5)$..............Answer

Answer 2

Its is (c/x,1/2)
 Because math works this way the answer is write! yay