Answer:
v = 7
is the value for which
x = (-21 - √301)/10
is a solution to the quadratic equation
5x² + 21x + v = 0
Explanation:
Given that
x = (-21 - √301)/10 .....................(1)
is a root of the quadratic equation
5x² + 21x + v = 0 ........................(2)
We want to find the value of v foe which the equation is true.
Consider the quadratic formula
x = [-b ± √(b² - 4av)]/2a ..................(3)
Comparing (3) with (2), notice that
b = 21
2a = 10
=> a = 10/2 = 5
and
b² - 4av = 301
=> 21² - 4(5)v = 301
-20v = 301 - 441
-20v = -140
v = -140/(-20)
v = 7
That is a = 5, b = 21, and v = 7
The equation is then
5x² + 21x + 7 = 0