find the sum and product of the roots of the equation 5x^2+11x-3=0 ?
recall that for
ax^2 + bx + c = 0
the sum of the roots = -b/a
the product of the roots = c/a
sum = -11/5 and product = -3/5
The sum of the roots is like a wild party where the roots are getting together and having a blast. To find the sum, we can use the formula:
Sum of roots = -b/a
In this case, a = 5 and b = 11. So, the sum of the roots would be:
Sum of roots = -11/5
Now, when it comes to the product of the roots, it's like they're multiplying their awesomeness together. To find the product, we can use another formula:
Product of roots = c/a
In our equation, c is -3 and a is 5. So, the product of the roots would be:
Product of roots = -3/5
So, the sum of the roots is -11/5 and the product of the roots is -3/5. Let's hope they don't cause any mischief together!
To find the sum and product of the roots of the equation 5x^2 + 11x - 3 = 0, we can use Vieta's formulas. Vieta's formulas state that for a quadratic equation in the form ax^2 + bx + c = 0 with roots α and β, the sum of the roots is -b/a and the product of the roots is c/a.
Comparing the given equation to the standard quadratic form, we have:
a = 5,
b = 11, and
c = -3.
Therefore, the sum of the roots is:
-sum of roots = -b/a = -(11/5) = -11/5.
And the product of the roots is:
product of roots = c/a = (-3)/5 = -3/5.
So, the sum of the roots is -11/5 and the product of the roots is -3/5.
To find the sum and product of the roots of the equation 5x^2 + 11x - 3 = 0, we can make use of Viète's formulas.
According to Viète's formulas, the sum of the roots of a quadratic equation in the form ax^2 + bx + c = 0 is given by the ratio of the coefficient of the linear term to the coefficient of the quadratic term, but with the opposite sign. In other words, the sum of the roots of the equation is -b/a.
Similarly, the product of the roots is given by the ratio of the constant term to the coefficient of the quadratic term, but with the opposite sign. In other words, the product of the roots is c/a.
In the given equation, 5x^2 + 11x - 3 = 0, we can identify that a = 5, b = 11, and c = -3.
Therefore, the sum of the roots is -b/a = -11/5 = -2.2.
And the product of the roots is c/a = -3/5.
Hence, the sum of the roots is -2.2 and the product of the roots is -3/5.