Question

The difference between the roots of the quadratic equation x^2−14x+q=0 is 6. Find q.

Answer 1

The value of q is 40

Step-by-step explanation:

In the quadratic equation ax² - bx + c = 0, where

• a = 1
• b is the sum of its two roots
• c is the product of its two roots

Assume that the roots of the quadratic equations are x and y

∵ The quadratic equation is x² - 14x + q = 0

∴ a = 1 , b = 14 and c = q

∵ b is the sum of its two roots

∵ Its roots are x and y

∴ x + y = 14 ⇒ (1)

∵ The difference between the roots is 6

∴ x - y = 6 ⇒ (2)

Now we have a system of equation to solve it

Add equations (1) and (2)

∴ 2x = 20

- Divide both sides by 2

∴ x = 10

Substitute the value of x in equation (1) or (2) to find y

∵ 10 + y = 14

- Subtract 10 from both sides

∴ y = 4

∵ c is the product of the two roots

∴ c = 10 × 4 = 40

∵ c = q

∴ q = 40

The value of q is 40

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly