Question

Find the value of K for the quadratic equation x^2-kx+36=0 so that it has two equal roots

Answer 1

Answer:

K =12

Step-by-step explanation:

consider alpha =p and beta=q

p+q=-b/a => -(-k)/1 = k

and

pq=c/a. => 36

given two roots are equal i.e. p=q

p+p = k => 2p =k

p=k/2

and also px p = p2 =36

p =+6

=> 2x 6= k

=>k=12

Hope this helps

Answer 2

Answer:

Value of k is +12 or -12

Step-by-step explanation:

Given equation is

${x}^{2} - kx + 36 = 0............(i)$

$Comparing \: equation \: (i) \: with \: equation \: a {x}^{2} + bx + c = 0$

We get,

a=1 , b= -k and c= 36

Now given condition is given equation has two equal roots, i.e

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

Value putting of a,b and c and get

${( - k)}^{2} = 4 \times 1 \times 36 \\ {k}^{2} = 4 \times 36 \\ k = + o \\ \: of - \sqrt{4 \times 36} = + \: or \: - \sqrt{4 \times 4 \times 3 \times 3} \\ k = + \:or - 12$

Therefore value of k is +12 or -12.