Question

if one root of the quadratic equation
$kx {}^{2} - 3x - 1$
is,
$\frac{1}{2}$
Then find the value of "k" ...





•Can you plz help me in this question to be solve..!

Answer 1

Answer:

k = 10

Step-by-step explanation:

Product of roots = Constant term / Coefficient of x²

Let the Other root be p

⇒ p*1/2 = -1/k ------------- (i)

Sum of Roots = - (Coefficient of x) / Coefficient of x²

⇒ p+1/2 = -(-3/k)

⇒ p+1/2 = 3/k ----------------(ii)

Now { 3*(i) } + (ii) ⇒ (3p/2) + p + 1/2 = 0

⇒ 5p/2 = -1/2

⇒ p = -1/5

⇒ Form (i) k = -2/p ⇒ k = -2*(-5) = 10

⇒ k = 10  

Answer 2

one way to find the value of k is that

for given quadratic equation.

x = -(-3) + root [(-3)^2 -4×k (-1)] / 2×k
this is the expression for finding root of quadratic equation....

now u r given value of one root i.e 1/2...

now put the value of x=1/2 in the above expression and solve it to find value of k...

Note: i have written the expression for finding one root only....the other root can also be found but in place of + sign after -3......it will be - sign.......
use that formula which can give you real and defined value of k....

there can be some more methods to solve......for this u can google it....u may find easier solution there....

thanks......
#innervoice...