The following quadratic equation has the integer solutions
x^2+5x-6=0
what is the positive solution of the equation
Factor left-hand side to get:
x²+5x-6=0
(x+6)(x-1)=0
Now equate each factor to zero and find x.
x+6=0 => x=-6
x-1=0 => x=1
From these solutions, find the positive solution.
to get the solution/roots, we can use quadratic formula:
x = [-b +- sqrt(b^2 - 4ac)]/(2a)
where
a = numerical coefficient of x^2
b = numerical coefficient of x
c = the constant
in the problem, x^2+5x-6 = 0, thus
a = 1, b = 5, c = -6
substituting:
x = [-b +- sqrt(b^2 - 4ac)]/(2a)
since we need the positive root, we choose the plus sign (we replace the plus/minus sign (+-) by plus sign (+) only):
x = [-5 + sqrt(5^2 - 4(1)(-6))]/(2(1))
x = [-5 + sqrt(25 + 24)]/2
x = [-5 + sqrt(49)]/2
x = (-5 + 7)/2
x = 1
hope this helps~ :)
To find the solutions of the quadratic equation x^2 + 5x - 6 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 1, b = 5, and c = -6. Substituting these values into the quadratic formula, we get:
x = (-(5) ± √((5)^2 - 4(1)(-6))) / (2(1))
Simplifying further, we have:
x = (-5 ± √(25 + 24)) / 2
x = (-5 ± √49) / 2
Now, we have two possible solutions:
1. x = (-5 + √49) / 2
x = (-5 + 7) / 2
x = 2 / 2
x = 1
2. x = (-5 - √49) / 2
x = (-5 - 7) / 2
x = -12 / 2
x = -6
Since we are looking for the positive solution, our answer is x = 1.