find the value of k for which 5x2+13x+k=0 have equal roots
Answers
Answered by
10
HI.
QUESTION
==> FIND THE VALUE OF k FOR WHICH 5x² + 13x + k = 0 HAVE EQUAL ROOTS ❓
SOLUTION
✏ CONDITION FOR EQUAL ROOTS IS
==> b² - 4ac = 0
ON COMPARING ax² + bx + c = 0 WITH ABOVE EQUATION,
WE HAVE,
5x² + 13x + k = 0
a = 5, b = 13, c = k
THIS IMPLIES,
b² - 4ac = 0
==> (13)² - 4(5)(k) = 0
==> 169 - 20k = 0
==> 20k = 169
==> k = 169/20
==> k = 8.45
OR,
We know Quadratic formula,
x = -b ± √b² - 4ac / 2a
==> x = -b ± √0 / 2a.........{For equal roots}
==> x = (-13) ± 0 / 2(5)
==> x = -13 + 0 / 10 OR x = -13 - 0 / 10
==> x = -13/10 OR x = -13/10
This implies
( x + 13/10)(x + 13/10) = 5x² + 13x + k = 0
==> (x + 13/10)² = 5x² + 13x + k = 0
Taking LHS
==> x² + 2(13/10)x + (13/10)²
==> x² + 13x/5 + 169/100
on multiplying whole equation with 5,
==> 5x² + 13x + 169/20
==> 5x² + 13x + 8.45
THUS, k = 169/20 OR k = 8.45
HOPE IT HELPS YOU.
QUESTION
==> FIND THE VALUE OF k FOR WHICH 5x² + 13x + k = 0 HAVE EQUAL ROOTS ❓
SOLUTION
✏ CONDITION FOR EQUAL ROOTS IS
==> b² - 4ac = 0
ON COMPARING ax² + bx + c = 0 WITH ABOVE EQUATION,
WE HAVE,
5x² + 13x + k = 0
a = 5, b = 13, c = k
THIS IMPLIES,
b² - 4ac = 0
==> (13)² - 4(5)(k) = 0
==> 169 - 20k = 0
==> 20k = 169
==> k = 169/20
==> k = 8.45
OR,
We know Quadratic formula,
x = -b ± √b² - 4ac / 2a
==> x = -b ± √0 / 2a.........{For equal roots}
==> x = (-13) ± 0 / 2(5)
==> x = -13 + 0 / 10 OR x = -13 - 0 / 10
==> x = -13/10 OR x = -13/10
This implies
( x + 13/10)(x + 13/10) = 5x² + 13x + k = 0
==> (x + 13/10)² = 5x² + 13x + k = 0
Taking LHS
==> x² + 2(13/10)x + (13/10)²
==> x² + 13x/5 + 169/100
on multiplying whole equation with 5,
==> 5x² + 13x + 169/20
==> 5x² + 13x + 8.45
THUS, k = 169/20 OR k = 8.45
HOPE IT HELPS YOU.
Anonymous:
Aree.. vah! Great answer ❤
Answered by
33
Hii ☺ !
5x² + 13x + k = 0
Here,
a = 5 , b = 13 and c = k
Discriminant ( d ) = 0
b² - 4ac = 0
13² - 4 × 5 × k = 0
169 - 20k = 0
-20k = -169
k = 169/20 [ Answer ]
5x² + 13x + k = 0
Here,
a = 5 , b = 13 and c = k
Discriminant ( d ) = 0
b² - 4ac = 0
13² - 4 × 5 × k = 0
169 - 20k = 0
-20k = -169
k = 169/20 [ Answer ]
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