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CBSE Class 10 Answered

If the roots of the equation (b-c)x^2 + (c-a)x + (a-b)=0 are equal,then prove that 2b=a+c
Asked by | 29 Jan, 2014, 05:02: PM
answered-by-expert Expert Answer
For equal roots, discriminant should be 0. So, (c-a)² - 4(b-c)(a-b)= 0 c² - 2ac + a² - 4ab + 4b² + 4ac - 4bc = 0 c² + 2ac + a² + 4b² - 4ab - 4bc = 0 (c + a)² + 4b² - 4b(a + c) = 0 [(a + c) - (2b)]² = 0 Hence, 2b = a + c
Answered by | 29 Jan, 2014, 05:39: PM
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