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Standard X

Mathematics

Sum of N Terms of an AP

For what posi...

Question

For what positive values of m the equation $(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0$ has equal roots.

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Solution

Given equation is $(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0$ ...(i)
Let $D$ be the discriminant of equation (i).
Roots of equation (i) will be equal if $D = 0.$
or $4 {(1 + 3 m)}^{2} - 4 (1 + m) (1 + 8 m) = 0$
or $4 (1 + 9 m^{2} + 6 m - 1 - 9 m - 8 m^{2}) = 0$
or $m^{2} - 3 m = 0$ or, $m (m - 3) = 0$
$∴$ $m = 0, 3.$

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For what positive values of m the equation (1+m)x2−2(1+3m)x+(1+8m)=0 has equal roots.

Given equation is (1+m)x2−2(1+3m)x+(1+8m)=0 ...(i)Let D be the discriminant of equation (i).Roots of equation (i) will be equal if D=0.or 4(1+3m)2−4(1+m)(1+8m)=0or 4(1+9m2+6m−1−9m−8m2)=0or m2−3m=0 or, m(m−3)=0∴ m=0,3.

For what positive values of m the equation $(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0$ has equal roots.