Answer:
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
