Question

1. Show that X = 1 is the root of the polynomial 2 x³-3x²+7x-6.

2. If X = 2 is a root of the polynomial f(X) =2x³-6x²+5x+m,find the value of m.

# ItzYourQueen01​

Answer 1

f(x) = 2 x³-3x²+7x-6

1.

if x = 1 is a root of the polynomial

So, f(1) = 0

Therefore,

$2 \times {1}^{3} - 3 \times {1}^{2} + 7 \times 1 - 6 = 0 \\ 2 - 3 + 7 - 6 = 0 \\ 9 - 9 = 0 \\ 0 = 0$

Hence,

X = 1 is the root of the polynomial 2x³-3x²+7x-6.

2.

Since, x = 2 is root of f(x) = 2x³-6x²+5x+m

So, f( 2) = 0

$2 \times {2}^{3} - 6\times {2}^{2} + 5 \times 2 + m = 0 \\ 2 \times 8 - 6\times 4 + 10 + m = 0 \\ 16 -24 + 10 + m = 0 \\ 26 - 24 + m = 0 \\ 2 + m = 0 \\ m = - 2$

hope it will help u ✨☺️