Question

anyone knows thd answer of 2nd and 3rd . how to solve .plz ans

Answer 1

2. Alpha + beta = - coefficient of x / coefficient of x^2.
Alpha + beta = - ( -b) / a = b / a.
3.
Let p (x) = 3x^2 + 2kx - 3.
Now
P (-1/2 ) = 3* ( -1/2 )^2 + 2 * -1/2 * k -3.
= 3 * 1/4 - k - 3.
= 3/4 -3 - k
= -9/4 - k

Now,
As -1/2 Is the zero of the polynomial thus remainder will be equal to 0.
Thus,
-9/4 -k = 0
k = - 9/4.