Step-by-step explanation:
We have the roots 1/2 and 4/3 and we need to write a quadratic equation of the form a x^{2} +bx+cax
2
+bx+c using those roots. Since we know that 1/2 and 4/3 are roots of our quadratic, we can equate each root to xx and factor backwards:
x= \frac{1}{2}x=
2
1
and x= \frac{4}{3}x=
3
4
2x=12x=1 and 3x=43x=4
2x-1=02x−1=0 and 3x-4=03x−4=0
Now we can multiply the left sides of our equations to get our quadratic:
(2x-1)(3x-4)=6 x^{2} -8x-3x+4=6 x^{2} -11x+4(2x−1)(3x−4)=6x
2
−8x−3x+4=6x
2
−11x+4
W can conclude that the quadratic equation with roots 1/2 and 4/3 is 6x^2-11x+46x
2
−11x+4
