Question

find the values of m for which the quadratic equation X square - 2 x minus 8 minus 15 equal to zero has equal roots and both roots positive

Answer 1

Step-by-step explanation:

Answer

Both roots are equal , it means discriminant of quadratic equation is zero.

given quadratic equation , x² - m(2x - 8) - 15 = 0

x² - 2mx + 8m - 15 = 0

x² - 2mx + (8m - 15) = 0

Now, discriminant , D = (-2m)² - 4(8m - 15) = 0

4m² - 32m + 60 = 0

m² - 8m + 15 = 0

m² - 5m - 3m + 15 = 0

(m - 5)(m - 3) = 0

m = 5 and 3

Case 1 :- take m = 5

x² - 5(2x -8) - 15 = 0

x² -10x + 40 - 15 = 0

x² - 10x + 25 = 0

Both roots are positive and x = 5

Hence, m = 5 is possible value .

Case 2 :- take m = 3

x² - 3(2x - 8) - 15 = 0

x² - 6x + 24 - 15 = 0

x² - 6x + 9 = 0

Both roots are positive and x = 3

so, m = 3 is also possible value.

Hence, m = 3 and 5

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