Question

if the roots of equations (a-b)x²+(b-c)x+(c-a)=0 are equal prove that b+c =2a
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Answer 1

Answer:

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Step-by-step explanation:

If the quadratic equation=ax²+bx+c=0 whose roots are equal then it's deteminant is equal to zero. Hence proved.

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Answer 2

Hello,

AKASHITEMHEAVEN HERE,

The question must be, if roots of equation (a-b)x2+(b-c)x+(c-a)=0 are equal , prove that b+c = 2a.

Using Discriminant,

D = B2-4AC as compared with the general quadratic equation Ax2+Bx+C=0

so, A = a-b

B = b-c

C = c-a

For roots to be equal, D=0

(b-c)² - 4(a-b)(c-a) =0

b²+c²-2bc -4(ac-a²-bc+ab) =0

b²+c²-2bc -4ac+4a²+4bc-4ab=0

4a²+b²+c²+2bc-4ab-4ac=0

(2a-b-c)²=0

i.e. 2a-b-c =0

2a= b+c

Hence proved.

Hope it helps

Thanks