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masha68 [24]
4 years ago
10

The difference between the roots of the quadratic equation x2−14x+q=0 is 6. Find q.

Mathematics
2 answers:
zzz [600]4 years ago
6 0

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.

<u>To recap:</u>

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

erastova [34]4 years ago
6 0

Answer:

q=40

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:

ax^{2}+bx+c=0

Since x' and x'' are the roots of this equation, then we can write the Vieta's formula:

\left\{\begin{matrix}x'+x''=\frac{-b}{a} & \\ x'*x''=\frac{c}{a} & \end{matrix}\right.\\

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.

\left\{\begin{matrix}x'+x''=\frac{14}{1} & \\ x'-x''=6 & \end{matrix}\right.\Rightarrow 2x'=20\therefore x'=10

3) Solving the system:

10+x''=14\Rightarrow x''=14-10\Rightarrow x''=4

4) Since we have a=1:

x^{2}-14x+q=0

Then we can make q as the parameter c.

q=x'*x''=4*10\therefore q=40

x^{2}-14x+40=0

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You need to find the value of 'x'.
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Substitute into equation
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Please double check this.
Hope this helps :)
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Igoryamba

Answer:

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Step-by-step explanation:

In 6 years, 12 years will be added to the total of their ages, so it will be 72. Since this is the total of Mark's age and twice Mark's age, his age at that time will be 72/3 = 24. His mother will be 48 at that time.

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Step-by-step explanation:

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The point on the scaled, translated graph will be ...

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Based on the amount that Nader can pay per month, and the interest rate as well as the period, the amount he could spend if the rate was annual is $8,385.33.

<h3 /><h3>How much could Nader spend on the car?</h3>

If Nader can pay $280 per month, the amount he can pay per year i:

= 280 x 12

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The amount that he can spend on the car is the present value of these yearly payments:

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= 3,360 x 2.49563439768461

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Find out more on the present value of periodic payments at brainly.com/question/17244776.

#SPJ1

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