the other two zeroes of the polynomial x3 - 8x2 + 19x -12 if its one zeroes is x=1 :- - Maths - Polynomials

Question

the other two zeroes of the polynomial x3 -
8x2 + 19x -12 if its one zeroes is x=1 :-

Gursheen kaur. · Accepted Answer

$T h e g i v e n p o l y n o m i a l i s x^{3} - 8 x^{2} + 19 x - 12$

As, it is given that,

one zeros = 1

that is, (x-1) is the root of the given polynomial.

$t h e r e f o r e, b y l o n g d i v i s i o n m e t h o d, x - 1 \begin{matrix} x^{2} - 7 x + 12 \\ x^{3} - 8 x^{2} + 19 x - 12 \end{matrix} x^{3} - x^{2} \bar{- +} - 7 x^{2} + 19 x - 12 - 7 x^{2} + 7 x \bar{+ -} 12 x - 12 12 x - 12 \bar{} 0$

$x^{2} - 7 x + 12 = 0 x^{2} - 4 x - 3 x + 12 = 0 x (x - 4) - 3 (x - 4) = 0 (x - 3) (x - 4) = 0 e i t h e r x - 3 = 0 o r x - 4 = 0 x = 3 o r x = 4$

thus, the other roots are 3 and 4