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`

`(3x^2-4x+15)/(3)= (0)/(3)`

`(3x^2)/(3)-(4x)/(3)+(15)/(3)= (0)/(3)`

now, we can simplify it

`x^2-(4)/(3)x+5= 0`

now, we can compare it with

`x^2+bx+c=0`

we get

`b=-(4)/(3)`

`c=5`

so, we get order pair as

`(b,c)=(-(4)/(3) , 5)`..............Answer