Question

If 2 and 3 are zeroes of the polynomial 3x^2-2kx +2m find the value of k and m

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

p(x) = 3x² - 2kx + 2m

$\textbf{\underline{According\;to\;Information}}$

Zeroes of p(x) = 2 and 3

Hence ,

p(2) = 0

Also,

p(3) = 0

$\textbf{\underline{Hence, }}$

p(2) = 3 × 2² - 2k(2) + 2m = 0

3 × 4 - 4kx + 2m = 0

12 - 4k + 2m = 0………..(1)

$\textbf{\underline{Now, }}$

p(3) = 3 × 3² - 2k(3) + 2m = 0

3 × 9 - 6kx + 2m = 0

27 - 6k + 2m = 0………..(2)

$\textbf{\underline{Subtracting\;(2)\;from\;(1)\;we\;get:-}}$

15 - 2k = 0

15 = 2k

$\tt{\rightarrow k=\dfrac{15}{2}}$

Substituting value of k in (1)

12 - 4k + 2m = 0

$\tt{\rightarrow 12-4\dfrac{15}{2}+2m=0}$

12 - 30 + 2m = 0

-18 + 2m = 0

2m = 18

$\tt{\rightarrow m=\dfrac{18}{2}}$

m = 9

Therefore we get,

$\tt{\rightarrow k=\dfrac{15}{2}\;and\;m=9}$