Question

find the value of k so that the equation 2 x square - 10 X + K is equal to zero has real and equal roots​

Answer 1

Answer:

12.5

Step-by-step explanation:

Given Quadratic equation is 2x² - 10x + k = 0.

Here, a = 2, b = -10, c = k.

Given that Equation has real and equal roots.

∴ b² - 4ac = 0

⇒ (-10)² - 4(2)(k) = 0

⇒ 100 - 8k = 0

⇒ 100 = 8k

⇒ (100/8) = k

⇒ k = 12.5

∴ Therefore, value of k = 12.5

Hope it helps!

Answer 2

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K = $\frac{25}{2}$

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step-by-step explanation:

Given,

a quadratic equation:-

$2{x}^{2}-10x+k=0$

we know that,

standard form of a quadratic equation is

$a{x}^{2}+bx+c=0$

so comparing the given equation,

we get,

a = 2

b = -10

c = k

Now,

we know that,

for real and equal roots,

Descriminant, D = 0

=> ${b}^{2}-4ac=0$

now,

putting the respective values,

we get,

=> ${(-10)}^{2}-4×2×k=0$

=> 100 - 8k = 0

=> 8k = 100

=> k = 100/8

=> k = 25/2

Hence,

for real and equal roots,

the value of,

K = $\frac{25}{2}$

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