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

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

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!