Question

Solve the following briefly : [2 marks each]
1. Check if 1 and 3 are the zeroes of the polynomial x3 - 6x2 + 11x-6.​

Answer 1

QUESTION :

• Check if 1 and 3 are the zeroes of the polynomial $\bf{x ^3 - 6x^2 + 11x-6}$ .

SOLUTION :

REQUIRED KNOWLEDGE :

• If 1 and 3 are the zeros of the given polynomial then putting these values we will get p(x) = 0 ,i.e. p(1) = 0 and p(3) =0 .

Now,

$\implies \sf{p(x) =x ^3 - 6x^2 + 11x-6 }$

$\implies \sf{p(1) =(1 )^3 - 6 \times (1)^2 + 11 \times 1-6 }$

$\implies \sf{p(1) =1 - 6 \times 1+ 11 \times 1-6 }$

$\implies \sf{p(1) =1 - 6 + 11-6 }$

$\implies \sf{p(1) =12 - 12 }$

$\implies \underline{\huge{ \red{\bf{p(1) =0} }}}$

____________________________

$\implies \sf{p(x) =x ^3 - 6x^2 + 11x-6 }$

$\implies \sf{p(3) =(3)^3 - 6 \times (3)^2 + 11 \times 3-6 }$

$\implies \sf{p(3) =27 - 6 \times 9+ 11 \times 3-6 }$

$\implies \sf{p(3) =27 - 54 + 33-6 }$

$\implies \sf{p(3) =60 - 60 }$

$\implies \underline{ \huge {\red{\bf{p(3) =0} }}}$

$\huge{ \pink{\therefore}}$1 and 3 are the zeros of the given polynomial .