IGNOU MTE 3 2018 - For what values of m will the equationx 2 − 2x (1 + 3m) + 7

Question

For what values of m will the equation

x² − 2x (1 + 3m) + 7 (3 + 2m) = 0

have equal roots?

02 Feb 2018

Answer :

Word Count : 390

We are given the quadratic equation: \[ x^2 - 2x(1 + 3m) + 7(3 + 2m) = 0 \] To determine the value(s) of \( m \) that make the equation have equal roots, we can use the discriminant condition for a quadratic equation \( ax^2 + bx + c = 0 \), where the discriminant is given by: \[ \Delta = b^2 - 4ac \] For equal roots, the discriminant \( \Delta \) must be zero. Let’s first rewrite the given equation in the standard quadratic form: \[ x^2 - 2x(1 + 3m) + 7(3 + 2m) = 0 \] Expanding it: \[ x^2 - 2x(1 + 3m) + 7(3 + 2m) = x^2 - 2x - 6mx + 21 + 14m \] Thus, the quadratic equation becomes: \[ x^2 - (2 + 6m)x + (21

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