Question

If the roots of th eqation (b-c)x^2+(c-a)x+(a-b)=0 are equal.
Then Prove : 2b=a-c

NO SPAM​

Answer 1

Answer:

hope u like it......✌️

Answer 2

Given :-

• Roots of th eqation (b-c)x²+(c-a)x+(a-b)=0 are equal.

To Prove :-

• 2b = (a + c).

Solution :-

(b-c)x² + (c-a)x + (a-b) = 0

Comparing with quadratic equation Ax²+Bx+C = 0,,

→ A = (b - c)

→ B = (c - a)

→ C = (a - b)

Now, we know That, Discriminate when roots are equal is Equal to Zero.

→ D = B² - 4AC = 0

→ (c - a)²−4(b - c)(a - b) = 0

→ (c²+a² - 2ac) - 4(ba- ac- b²+bc) = 0

→ c²+a²- 2ac - 4ab+ 4ac +4b²- 4bc = 0

→ c²+a²+2ac - 4b(a+c) + 4b² = 0

→ (a+c)²- 4b(a+c)+4b² = 0

→ [(a+c)-2b]² = 0

→ (a+c) = 2b (Hence, Proved ).