Question

For what values of m will the equation x2+mx-(m 2+m-32)=0 has equal roots

Answer 1

plz clarify if it is m square or 2m

Answer 2

I guess when you say that a quadratic equation has equal values, you actually mean the equation having identical roots. I attempt my answer with this understanding but just in case I am mistaken, I am sorry.

A quadratic equation of the form ax^2+bx+c=0 has identical roots when its discriminant: b2−4ac equals 0 .

Upon comparing your equation with the standard form, a=1,b=m and c=−(m2+3m−32)

So, we have that, for the equation x2+mx−(m^2+3m−32) to have identical roots, m must satisfy the equation m2+4(1)(m2+3m−32)=0

⇒m^2+4m2+12m−128=0

⇒5m2+12m−128=0

This itself is a quadratic equation in m , and by the theory of quadratic equations, the roots of this equation are

−12±122+4×5×128−−−−−−−−−−−−−−√2×5

=−12±144+2560−−−−−−−−−√10=−12±2704−−−−√10

=−12±5210

So, the possible values of m are −12−5210 and −12+5210

or, −6410 and 4010

or, −32/5 and 4