The roots of
x^2 + 5x + 3 = 0 are p and q, and the roots of
x^2 + bx + c = 0 are p^2 and q^2. Find b + c.
I didn't get it, I need an answer quick. I tried plugging in those answers for b and c, it just got more complex. Please get an answer quick
This is urgent, it is due tonight
Please! I really need an answer quick!
To find the value of b + c, we need to determine the values of b and c individually. Given that the roots of x^2 + 5x + 3 = 0 are p and q, we can use the fact that the sum and product of the roots relate to the coefficients of the quadratic equation.
For any quadratic equation of the form ax^2 + bx + c = 0, the sum of the roots (p and q), denoted by S, is given by:
S = -b/a
And the product of the roots (p and q), denoted by P, is given by:
P = c/a
In this case, the equation is x^2 + 5x + 3 = 0, so we have:
S = -5/1 = -5
P = 3/1 = 3
Next, we need to find the sum and product of the roots of the equation x^2 + bx + c = 0, which are p^2 and q^2. According to Vieta's formulas, the sum and product of the roots relate to the coefficients in a similar manner:
Sum of the roots (p^2 and q^2), denoted by S', is given by:
S' = -b/a
Product of the roots (p^2 and q^2), denoted by P', is given by:
P' = c/a
Since we're interested in the values of b and c, we can set S' and P' equal to -5 and 3 respectively:
S' = -5
P' = 3
Therefore, we have the following equations:
-b/a = -5
c/a = 3
To find b and c, we need another equation relating them. Fortunately, we can square the equation -b/a = -5:
(-b/a)^2 = (-5)^2
b^2/a^2 = 25
Since c/a = 3, we can write c = 3a.
Substituting c = 3a in the equation b^2/a^2 = 25:
b^2/a^2 = 25
b^2 = 25a^2
Taking the square root of both sides:
b = ±5a
This implies that b can be written as ±5a.
Now, since c = 3a, we can express b + c as:
b + c = ±5a + 3a
b + c = (±5 + 3)a
b + c = (±8)a
Therefore, b + c can be either 8a or -8a, depending on whether we take the positive or negative sign for b.
In conclusion, b + c is equal to ±8a, where a is a constant.
use the quadratic formula to find the roots of the 1st equation
then plug the numbers into the 2nd question