Question

1. Find the value of k in each of the following quadratic equations, for which the
given value of x is a root of the given quadratic equation.
(a) 3x2 - kx - 2 = 0, x = 2
(b) 14x² - 27x + k = 0; x = 5/2​

Answer 1

Answer:

(a) GIVEN

one root of the equation 3x2-kx-2=0 is 2

x = 2

Place the value of x in 3x2-kx-2=0

3(2)^2 - k(2) - 2 = 0

(3 x 4) - 2k - 2 = 0

12 - 2 - 2k = 0

10 - 2k = 0

10 = 2k

10 / 2 = k

5 = k

Now the equation is 3x^2 -5x - 2 = 0

Factorize :

3x^2 - 6x + x - 2 = 0

3x (x - 2) + 1 (x - 2) = 0

(3x + 1) (x - 2) = 0

3x + 1 = 0 & x - 2 = 0

3x = - 1 & x = 2

x = - 1 / 3 & x = 2

Therefore, the other root is - 1 / 3

(b)When we put the value of x as 5/2 we get Zero as resultant Coz it is given that 5/2 is the root of the equation

14x² - 27x + k = 0

Refer the pic....

Step-by-step explanation:

Hope it helps :)-