the roots of the equation X square - 15 - m into 2 x minus 8 is equals to zero are equal then M equal to
Answers
hey mate...
here is your 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
hope it helps...
as roots are equal , 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 =b^2-4ac= (-2m)² - 4(8m - 15)(1)= 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.
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