Find the values of m and n for which x = 2 and 3 are zeroes of the polynomial: 3x2 - Maths - Polynomials

Question

Find the values of m and n for which x = 2 and 3 are zeroes of
the polynomial: 3x2 2mx + 2n

Manbar Singh · Accepted Answer

The given quadratic polynomial is,px = 3x2 - 2mx + 2nSince x = 2 is
a zero of px, then p2 = 0⇒322 - 2m2 + 2n = 0⇒12 - 4m +
2n = 0⇒-4m + 2n = -12⇒2m - n = 6⇒n = 2m - 6
1Since x = 3 is a zero of px, then p3 = 0⇒332 - 2m3 + 2n =
0⇒27 - 6m + 2n = 0⇒-6m + 2n = -27 2putting the value of
n from 1 in 2, we get, -6m + 22m - 6 = -27⇒-6m + 4m - 12 =
-27⇒-2m = -15⇒m = 152from 1, we have,n = 2×152 -
6 = 15 - 6 = 9so, n = 9

Find the values of m and n for which x = 2 and 3 are zeroes of the polynomial: 3x2 2mx + 2n.