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3.19 The quadratic equation 16-012 (1-0)x+ (0-6)=0hos equal rool, then show that_2b=a+c |
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Answer» If roots of a quadratic EQUATION are equal, then DISCRIMINANT of the quadratic equation is 0 D=B 2 −4ac=0 (b−c)X 2 +(c−a)x+(a−b)=0 Comparing with ax 2 +bx+c=0 Here, a=(b−c), b=(c−a) and c=(a−b) So, ⇒(c−a) 2 −4(b−c)(a−b)=0 ⇒c 2 +a 2 −2ac−4(ab−b 2 −ac+bc)=0 ⇒c 2 +a 2 −2ac−4ab+4b 2 +4ac−4bc=0 ⇒c 2 +a 2 +2ac+4b 2 −4ab−4bc=0 ⇒(c+a) 2 +4b 2 −4b(a+c)=0 ⇒(c+a) 2 +(2b) 2 −2(c+a)(2b)=0 ⇒[(c+a)−(2b)] 2 =0 ⇒c+a−2b=0 ⇒2b=c+a |
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