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For what value of m, are the roots of the equation (3m + 1)x^2 + (11 + m) x + 9 = 0 equal? - Mathematics

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Sum

For what value of m, are the roots of the equation (3m + 1)x2 + (11 + m) x + 9 = 0 equal?

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Solution

Comparing the given equation with ax2 + bx + c = 0;

we get : a = 3m + 1, b = 11 + m and c = 9

∴ Discriminant, D = b2 – 4ac

= (11 + m)2 – 4(3m + 1) × 9

= 121 + 22m + m2 – 108m – 36

= m2 – 86m + 85

= m2 – 85m – m + 85

= m(m – 85) – 1 (m – 85)

= (m – 85) (m – 1)

Since the roots are equal, D = 0

⇒ (m – 85) (m – 1) = 0

⇒ m – 85 = 0 or m – 1 = 0

⇒ m = 85 or m = 1

Concept: Nature of Roots
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