Question

if 1 root of the quadratic equation 2x^2+kx-6 is 2 find the value of k also find the other root

Answer 1

Hi
Nice question

Question:-
If one root of the quadrant equation 2x² + kx - 6 is 2. Find the value of k and also find the other root.

Solution:-

If 2 is a root of the equation, then it must be satisfying the equation.

So
x = 2

Putting this value in the quadratic equation, we get

2x² + kx - 6 = 0
2(2)² + k(2) - 6 = 0
8 + 2k - 6 = 0
2 + 2k = 0
2k = -2
k = -1

Put this in quadratic equation

2x² - x - 6 = 0

By splitting the middle term

2x² - 4x + 3x - 6 = 0
2x (x - 2) + 3 (x - 2) = 0
(2x + 3)(x - 2) = 0

2x + 3 = 0
and
x - 2 = 0

x = -3/2 and x = 2

So the other root is -3/2

Hope this helps you.

Answer 2

Hey !!

P ( x ) = 2X² + KX - 6

P ( 2 ) = 2 × (2)² + K × 2 - 6

=> 8 + 2K - 6 = 0

=> 2K = -2

=> K = -1

Sum of zeroes = -b/a

Other root + 2 = 1 / 2

Other root = 1/2 - 2


Other root = 1-4/2 = -3/2