Question

For what value of k the system

y = x^2 - 6x + 37
y = -2x + k

has one solution?

Answer 1

Ans--->

k = 33

Given ---> y = x² - 6x + 37

y = - 2x + k

To find---> Value of k if system of

equation has one solution

Solution--->

y = x² - 6x + 37 ----------------(1)

y = -2x + k ----------------(2)

Putting y = -2x + k in equation (1)

-2x + k = x² - 6x + 37

=> x² - 6x + 2x + 37 - k = 0

=> x² - 4x + ( 37 - k ) = 0 -------------(3)

It is a quadratic equation so it has two roots but according to question system of equation has one solution. It means quadratic equation has equal roots

Now comparing equation(3) with

ax² + bx + c = 0

a = 1 , b = -4 , c = ( 37 - k )

Now equation (3) has equal roots so

b² - 4ac = 0

=> ( - 4 )² - 4 ( 1 ) ( 37 - k ) = 0

=> 16 = 4 ( 37 - k )

=> 4 = 37 - k

=> k = 37 - 4

=> k = 33

Answer 2

Answer:

Hello friends Here is your answer