E₁: a+b+c=0, if 1 is a root of a x^2+b x+c=0, E₂: b^2-a^2=2 a c , if , are the roots of a x^2+b x+c=0 Which of the following is true?

Step-by-step solution

Given that, 1 is a root of a x^2+b x+c=0 aligned & a+b+c=0 & E₁: a+b+c=0 is true. aligned Since , are the roots of aligned & a x^2+b x+c=0 & + =- b a and = & c a aligned On squaring both sides of equation (i) array rlrl & ( + )^2 & = b^2 a^2 ^2 + ^2 +2 & = b^2 a^2 & 1+2 ( c a ) & = b^2 a^2 & 2 c a & = b^2-a^2 a^2 & -a^2+b^2 & =2 a c & E₂: b^2-a^2 & =2 a c is true array E₁ and E₂ both are true.