Question

If 2 and 3 are the zeroes of the polynomial 3x²-2kx+2m, then find the values of k and m.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

Let p(x) = 3x²-2kx+2m

Given, 2 & 3 are zeroes of p(x).
Then , p (2) = 0 & p(3)= 0

Now, p(2)= 3×2²-2k(2)+2m=0

3× 4-4kx+2m=0

12-4k+2m=0………..(1)

p(3) =  3×3²-2k(3)+2m=0

3× 9-6kx+2m=0

27-6k+2m=0………..(2)

On Subtracting Equation 1 from equation 2.

27-6k+2m=0
12-4k+2m=0
(-)  (+) (-)
------------------
15-2k =0

15=2k

k= 15/2

On putting k= 15/2 in eq 1

12-4k+2m=0

12-4(15/2)+2m=0

12-30+2m=0

-18+2m=0

2m=18
m=18/2
m=9

Hence, k=15/2, m= 9

HOPE THIS WILL HELP YOU....