Find the value of k for which X square+ 5kx +16 =0 has two equal real roots?

Question

Answer

From the given equation x² + 5kx + 16 = 0

a = 1 , b = 5k , c = 16

So, by using the discriminant formula, we can find the value of 'k' friend..

As per the question, it has two equal real roots so,

b² - 4ac = 0

25k² - 4(1)(16) = 0

25k² = 64

k² = 64/25

k² = 8²/5²

k² = (8/5)²

k = ±√(8/5)²

k = ±8/5.

Answer

Answer

Answer

K=8/5

Answer

Introduction:
The given quadratic equation is X^2 + 5kX + 16 = 0. We have to find the value of k for which the given equation has equal real roots.

Explanation:
For a quadratic equation, ax^2 + bx + c = 0, the roots can be found using the quadratic formula, which is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

For the given equation, X^2 + 5kX + 16 = 0, the discriminant (b^2 - 4ac) should be equal to zero for the equation to have equal real roots. Thus,

(b^2 - 4ac) = (5k)^2 - 4(1)(16) = 25k^2 - 64

Now, we can equate this to zero to get the value of k for which the given equation has equal real roots:

25k^2 - 64 = 0

25k^2 = 64

k^2 = 64/25

k = ±8/5

Therefore, the value of k for which the given equation has equal real roots is k = ±8/5.

Conclusion:
The value of k for which X^2 + 5kX + 16 = 0 has equal real roots is k = ±8/5.

Answer

X^2 +5 kx+ 16 then a=1 b=5k  c=16  since the eqation has 2 equal roots D=o    b^ 2 _ 4ac =o on taking the value  5k^2 _4×1×16 =o    25k^2  €_64=o                      k^2 =64/25  =8^2/5^2      ,k=8/5 answer   ,    so value  the   k is 8/5

Answer

We have,
a=1,b=5k and c =16
it is given that roots are equal
i.e. d = b2-4ac
d= (5k)2-4(1)(16)
25k2-64. (-4*16=-64)
25k2= +64
k2=64/25
k=root 64/25
k=8/5 (ans.) (root of 64 is 8 while root of 25 is 5).

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