If a,b,c are integers and b²=4(ac+5d²), d €N then roots of the eqn ax²+bx+c=0 are
Looking back I see many posts by you involving the quadratic equation and its properties,
You have shown no sign that you have attempted any of them, nor did you indicate where your problems lie.
The intent of this forum is not to simply do homework or assignments for you.
for this one, here is a clue:
you are given:
b^2 = 4(ac + 5d^2)
or
b^2 - 4ac = 20d^2
doesn't b^2 - 4ac show up in the quadratic formula?
See if you can somehow work that in ....
A businessman paid 25,000.00 for 12 machines.Find the
1 coast of 10 machine of the same type
2 number of such machines 175,000.00 can buy
To find the roots of the quadratic equation ax² + bx + c = 0, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, we are given that b² = 4(ac + 5d²). We need to substitute this into the quadratic formula to determine the roots.
Since b² = 4(ac + 5d²), we can rewrite the quadratic formula as:
x = (-b ± √(4(ac + 5d²) - 4ac)) / (2a)
Simplifying further, we get:
x = (-b ± √(4ac + 20d² - 4ac)) / (2a)
Notice that the 4ac terms cancel out:
x = (-b ± √(20d²)) / (2a)
Simplifying further, we have:
x = (-b ± 2√(5)d) / (2a)
Now, we can simplify the expression:
x = -b/2a ± √(5)d/a
Therefore, the roots of the quadratic equation ax² + bx + c = 0 are:
x = (-b/2a) ± √(5)d/a
Note that the values of a, b, c, and d should be given to obtain the specific roots of the equation.