Question

find the value of k for each of the following quadratic equation so that they have 2 equal roots
kx(x-2)+0=0

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Answer 1

Step-by-step explanation:

Given equation is: kx(x−2)+6=0

kx 2 −2kx+6=0

Then a=k,b=−2k,c=6

Then b²−4ac=0

So (−2k) 2 −4k(6)=0 4k 2 −24k=0

4k(k−6)=0

k=0 and k=6

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VIBHOR JINDAL

Answer 2

Here Is Your Answer Mate.....;

kx(x – 2) + 6 = 0

or kx^2 – 2kx + 6 = 0

Comparing the given equation with ax√2 + bx + c = 0, we get

a = k, b = – 2k and c = 6

We know, Discriminant = b2 – 4ac

= ( – 2k)^2 – 4 (k) (6)

= 4k^2 – 24k

For equal roots, we know,

b^2 – 4ac = 0

4k^2 – 24k = 0

4k (k – 6) = 0

Either 4k = 0 or k = 6 = 0

k = 0 or k = 6

However, if k = 0, then the equation will not have the terms ‘x^2‘ and ‘x‘.

Therefore, if this equation has two equal roots, k should be 6 only

Hope it's Helpful....:)