Question

show that x=1 is the zero of the polynomial 2x^3-3x^2+7x-6​

Answer 1

Answer:

Given polynomial;

2x³ - 3x² + 7x - 6

If x = 1 is the zero of the polynomial, then on Substituting the value of x = 1, the remainder must come zero(0).

Here we go :

$\implies \sf 2x {}^{3} - 3 {x}^{2} + 7x - 6 \\ \\ \implies \sf 2(1) {}^{3} - 3( {1})^{2} + 7(1) - 6 \\ \\ \implies \sf 2 - 3 + 7 - 6 \\ \\ \implies \sf 9 - 9 \\ \\ \implies \sf 0$

Hence, we got remainder = 0.

Therefore, x = 1 is the zero of the polynomial.

Answer 2

Put the value of x=1 and keep the equation equal to zero
And solve it
If it gives out the solution zero
Then your answer is right
Hence proved