Respuesta :
Answer:
Step-by-step explanation:
In a quadratic equation, a rule known as Vieta's Theorem tells us that roots 1 and 2 (we'll call them x1 and x2) added up is equal to -b/a, and x1 multiplied by x2 is equal to c/a. because x1-x2 is 6, and x1+x2=-b/a, which is -(-14), or 14, we can use the substitution method to find out the roots of the equation, being 4 and 10. When putting these roots into the equation, we get that 4^2-14(4)+q=0, and 10^2-14(10)+q=0. We can simplify these equations to make -40+q=0, and adding 40 on both sides gets us that q=40.
To recap:
Vieta's Formula:
- root 1 + root 2 = -b/a
- root 1 * root 2 = c/a
use substitution to find the roots
enter the roots into the quadratic equation
solve the equation!
Answer: q = 40
Answer:
[tex]q=40[/tex]
Step-by-step explanation:
1)To answer this question we need to remember the Vieta's or Viete's Formula to find the the roots of a quadratic expression:
[tex]ax^{2}+bx+c=0[/tex]
Since x' and x'' are the roots of this equation, then we can write the Vieta's formula:
[tex]\left\{\begin{matrix}x'+x''=\frac{-b}{a} & \\ x'*x''=\frac{c}{a} & \end{matrix}\right.\\[/tex]
2) As the question gives a precious information. x'-x''=6, let's replace the 2nd equation of the Vieta's formula by that and make it a Linear System.
[tex]\left\{\begin{matrix}x'+x''=\frac{14}{1} & \\ x'-x''=6 & \end{matrix}\right.\Rightarrow 2x'=20\therefore x'=10[/tex]
3) Solving the system:
[tex]10+x''=14\Rightarrow x''=14-10\Rightarrow x''=4[/tex]
4) Since we have a=1:
[tex]x^{2}-14x+q=0[/tex]
Then we can make q as the parameter c.
[tex]q=x'*x''=4*10\therefore q=40[/tex]
[tex]x^{2}-14x+40=0[/tex]
