The equation 2x² + px - 6 = 0 has equal roots. find the value(s) of p as a surd in its simplest form.

Hello from MrBillDoesMath!

There is no p value that answers the question.  

Discussion:

Consider the quadratic ax^2 + b^x + c = 0. The solution is

x =  ( -b +\- sqrt(b^2-4ac)) /2a

If b^2-4ac is NOT zero then there are two values of x that solve the equation. In b^2-4ac = 0, then both roots are equal, so there is only one solution.

Taking a = 2, b = p, and c = -6, in the quadratic formula:

b^2 - 4ac = 0 =>                   ( again, = 0 for a single root)

p^2 - 4(2)(-6) = 0 =>

p^2 + 48 = 0 =>                

which has no real solution as p^2 >= 0, so p^2 +48 >= 48 which means that p^2 + 48 =0 is not possible

Regards,  

MrB

12

step-by-step explanation:

a triangle's   full angle is 180 degrees so 180 - 156 = 24. 24/2=12