Question

4. Show that the roots of
(x-a)(x-b)=c² are real​

Answer 1

Answer:

Since D is positive, the roots are real.

Step-by-step explanation:

The given equation is:

(x-a)(x-b)=c^2.

Solving it further...

x^2-bx-ax+ab=c^2.

x^2-x(a+b)+ab-c^2=0.

Now, applying the quadratic formula method...

Here, dicriminant=D=B^2-4AC

D=(a+b)^2-4(ab-c^2)

D=(a+b)^2-4ab+4c^2.

D= a^2+b^2+2ab-4ab+4c^2

D= a^2+b^2+4c^2-2ab.

which comes out to be positive for every real value of a, b and c.

Thus, D 1.e. b^2-4ac is positive, so we can say that the roots of the given equation will be real, not imaginary.

Hope it helps....:)

Please mark brainliest, it's damn correct!