Please Help me solve this problem...
Give exact and approximate solutions to three decimals places.
x^2 + 3x - 7 = 0
Thanks!!!
The roots are
x = [-b +/- sqrt (b^2-4ac)]/2a
In your case, a = 1, b = 3 and c = -7.
x = [-3 +/- sqrt37]/2
Compute and round off.
I am not sure that I understand.
To solve the quadratic equation x^2 + 3x - 7 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b +- sqrt(b^2 - 4ac)) / (2a)
In our case, a = 1, b = 3, and c = -7. Plugging these values into the quadratic formula, we get:
x = [ -3 +- sqrt(3^2 - 4(1)(-7)) ] / (2 * 1)
Simplifying further, we have:
x = [ -3 +- sqrt(9 + 28) ] / 2
x = [ -3 +- sqrt(37) ] / 2
Therefore, the exact solutions to three decimal places are:
x ≈ ( -3 + sqrt(37) ) / 2
x ≈ ( -3 - sqrt(37) ) / 2
To find the approximate solutions to three decimal places, you can use a calculator to evaluate the square root of 37 and perform the necessary calculations.