If the sum of the roots of the equation ax^2 + bx + c = 0 is equal to the sum of their squares, then which one of the following is correct ? -Maths 9th

If the sum of the roots of the equation ax^2 + bx + c = 0 is equal to the sum of their squares, then which one of the following is correct ? -Maths 9th
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Answer :

Given equation: ax2+bx+c=0 Let α and β be the roots of given quadratic equation Sum of the roots i.e. α+β=a−b​Product of roots i.e. αβ=ac​It is given that, Sum of the roots = Sum of squares of the roots i.e. a−b​=α2+β2 i.e. a−b​=(α+β)2−2αβ i.e. a−b​=(a−b​)2−a2c​i.e. −ab=b2−2ac i.e. ab+b2=2ac Hence, C is the correct option.
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