Math, asked by kt290739, 5 months ago

find the value of k for the following quadratic equation so that it has two real and equal roots 5x²-2kx+20 =0​

Answers

Answered by amansulaniya
132

Answer:

5x2−2kx+20=0

It is given that the roots of the quadratic equation are real and equal, Then discriminant D=0.

Comparing the given equation with ax2+bx+c=0

we have a=5,b=−2k and c=20

Now, D=0

∴b2−4ac=0

∴(−2k)2−4(5)(20)=0

∴4k2−400=0

∴k2=100

∴k=±10

Thus, k=10 or −10

Step-by-step explanation:

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Answered by amitnrw
3

Given : 5x²-2kx+20 =0​

two real and equal roots

To Find : value of k

Solution:

Let say Equal roots are

α , α

Product of roots  =  α. α   = 20/5

=>  α²  = 4

=> α = ± 2

Sum of roots = α + α  = 2α

= 2 ( ± 2)

= ± 4

Sum of roots =  - (-2k)/5

= 2k/5

2k/5 =  ± 4

=> k =  ± 10

Value of k =  ± 10

Another method :

Roots are equal if D = 0

=> (-2k)² - 4(5)(20) = 0

=> 4k² - 400 = 0

=> k² - 100 = 0

=> (k + 10)(k - 10) = 0

=> k = 10 , - 10

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