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If the roots of the quadratic equation (b-c)x2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c |
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Answer» We have the equation (b-c)x²+(c-a)x+(a-b)=0 Comparing with quadratic equation Ax²+Bx+C=0 A=(b-c), Discriminate when roots are equal D=B²-4AC=0 D=(c-a)²−4(b-c)(a-b)=0 D=(c²+a²−2ac)-4(ba-ac-b²+bc)=0 D=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 |
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