Question

8. For each equation, given below, find the
value of 'm' so that the equation has
equal roots. Also, find the solution of each
equation:
(1) (m – 3)2 - 4x + 1 = 0
(ii) 3x² + 12x + (m + 7) = 0
(iii) x2 - (m + 2)x + (m + 5) = 0
​

Answer 1

Solution I:-

(m – 3)2 - 4x + 1 = 0

Since, It has equal Roots.

=) Discriminant ( d) = 0

=) b² - 4ac = 0

=) ( -4 )² - 4[ (m – 3)2 × 1 ] = 0

=) 16 - 4 ( 2m - 6) = 0

=) 16 - 8m + 24 = 0

=) 8m = 40

=) m = 40/8

=) m = 5

Solution II:-

3x² + 12x + (m + 7) = 0

Since, It has equal Roots.

=) Discriminant (d) = 0

=) b² - 4ac = 0

=) 12² - 4 [ 3 × (m+7) ] = 0

=) 144 - 4 ( 3m + 21) = 0

=) 144 - 12m - 84 = 0

=) 12m = 144 - 84

=) m = 60/12

=) m = 5

Solution III:-

x² - (m + 2)x + (m + 5) = 0

Since, It has equal Roots.

=) Discriminant (d) = 0

=) b² - 4ac = 0

=) ( m + 2)² - 4(m+5) = 0

=) m² + 4 + 4m - 4m - 20 = 0

=) m² - 16 = 0

=) m² = 16

=) m = 4.