Question

find the value of k for which 5x2+13x+k=0 have equal roots

Answer 1

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.

Answer 2

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 ]