Use "completing the square" to find the zeros of the polynomial.
=2x squared + 6x + 5 = 0
correction of problem. Should be:
-2x squared + 6x + 5 = 0
Sorry about that!
Thanks for your help!
well, this one is different anyway
-2 x^2 + 6 x + 5 = y find zeros
x^2 - 3 y - 2.5 - -y/2
x^2 - 3 y = -y/2 + 5/2
x^2 -3 y + 9/4 = -2 y/4 + 10 y/4 + 9/4
(x- 3/2)^2 = -1/2 (y -19/2)
when y = 0
(x-3/2)^2 = 19/4
so
x = 3/2 +/- 1/2 sqrt 19
check with quad eqn
x = [ -6 +/- sqrt (36 +40) ]/-4
= 3/2 +/- sqrt (76)/4
= 3/2 +/- 2 sqrt 19/4
= 3/2 +/- (1/2) sqrt 19 sure enough
To find the zeros of the polynomial 2x^2 + 6x + 5 = 0 using the method of completing the square, follow these steps:
Step 1: Ensure the leading coefficient is 1.
If the leading coefficient is not 1, divide the entire equation by 2 to make it 2x^2 + 3x + 2.5 = 0.
Step 2: Rearrange the equation.
Move the constant term (5 or 2.5) to the right side of the equation:
2x^2 + 6x = -5 or 2x^2 + 3x = -2.5
Step 3: Divide the coefficient of x by 2, square it, and add it to both sides of the equation.
Take half of the coefficient of x, which is 6/2 = 3, square it, which gives 3^2 = 9, and add it to both sides of the equation:
2x^2 + 6x + 9 = -5 + 9 or 2x^2 + 3x + 9 = -2.5 + 9
Step 4: Factor the left side of the equation.
The left side of the equation can be factored as a perfect square:
(√(2x^2 + 6x + 9))^2 = 4 or (√(2x^2 + 3x + 9))^2 = 6.5
Step 5: Simplify the right side of the equation.
Now, simplify the right side of the equation:
(√(2x^2 + 6x + 9))^2 = 4 simplifies to 2x^2 + 6x + 9 = 4 or (√(2x^2 + 3x + 9))^2 = 6.5 simplifies to 2x^2 + 3x + 9 = 6.5.
Step 6: Solve for x.
To solve the equations, isolate x on one side and take the square root of both sides:
2x^2 + 6x + 9 = 4
2x^2 + 3x + 9 = 6.5
Solving these equations will give you the values of x, which are the zeros of the original polynomial.