Assuming that the roots of the given qudratic equation are a, b find the sum and product of the roots.

Sum of root a+b = -c/d

Product of root ab= e/d

Step-by-step explanation:

Let the general quadratic equation be dx² + cx + e = 0

And the root of the equation be

'a' and 'b'

Using the general formula to find the solution to the quadratic equation

a = -c+√c²- 4de/2d

b = -c-√c²- 4de/2d

Taking the sum of the roots

a+b = (-c+√c²- 4de/2d) + (-c-√c²- 4de/2d)

a+b = (-c-c+√c²- 4de/2d - √c²- 4de/2d)/2d

a+b = -2c/2d

a+b = -c/d

The sum of the root of the quadratic equation will be -c/d

Product of roots

ab = (-c+√c²- 4de/2d)(-c-√c²- 4de/2d)

= {c² +(c√c²- 4de)- (c√c²- 4de) -(c²-4de)}/4d²

= {c²-c²+4de}/4d²

= 4de/4d²

= e/d

The product of the above quadratic equation will be e/d

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

yes

step-by-step explanation: