Mathematics: Write a quadratic equation with the given roots. write the equation in the form ax^2+bx+c=0 where a, b, and c are integers. 1/2, 4,3 a. 1/2x^2-4/3x+4=0 b. x^2 - 8x + 3 = 0 c. -6x^2 - 11x - 4 = 0 d.-6x^2 - 11x - 4 = 0

Write a quadratic equation with the given roots.

Ответ:

brasherfamily14

14.03.2022

We have the roots 1/2 and 4/3 and we need to write a quadratic equation of the form $a x^{2} +bx+c$ using those roots. Since we know that 1/2 and 4/3 are roots of our quadratic, we can equate each root to

and factor backwards:
$x= \frac{1}{2}$ and $x= \frac{4}{3}$
2x=1

and

and

Now we can multiply the left sides of our equations to get our quadratic:
$(2x-1)(3x-4)=6 x^{2} -8x-3x+4=6 x^{2} -11x+4$

W can conclude that the quadratic equation with roots 1/2 and 4/3 is 6x^2-11x+4