Question

If one zero of quadratic polynomial is x^2-5x-6 is 6 then find the other 0

Answer 1

Given:

• One zero of quadratic polynomial is 6.
• The quadratic polynomial is x²-5x-6.

To Find:

• The other zero of the quadratic polynomial.

Answer:

Given quadratic polynomial is x²-5x-6 .

When we equate a quadratic polynomial with 0 , then it becomes quadratic equation.

If 6 is a zero of polynomial , then (x-6) will be a factor of polynomial.

On dividing the polynomial with 0,

$\sf{\leadsto \dfrac{x^2-5x-6}{x-6}}$

$\sf{\leadsto \dfrac{x^2-6x+x-6}{x-6}}$

$\sf{\leadsto \dfrac{x(x-6)+1(x-6)}{x-6}}$

$\sf{\leadsto\dfrac{(x+1)\cancel{(x-6)}}{\cancel{x-6}}}$

$\bf{\leadsto x+1}$

Hence on equating with 0 ,

$\sf{\implies x +1=0}$

$\sf{\implies x = 0-1}$

${\underline{\boxed{\red{\bf{\longmapsto x=(-1)}}}}}$

Hence the other zero is (-1).

Answer 2

Step-by-step explanation:

$\sf \red {\underline{\underline{Given:-}}}$

• A quadratic polynomial x² - 5x - 6

• One of the zero of the quadratic polynomial is 6

$\sf \blue {\underline{\underline{To\:Find:-}}}$

• The other zero of the polynomial

$\sf \green {\underline{\underline{Solution:-}}}$

Given, one of the zero is 6

$\rm \pink{Let \: the \: other \: zero \: be \: (y)}$

$\rm sum \: of \: zeroes \: = 6 + y$

$\rm Product\: of \: zeroes \: = 6 (x) = 6y$

$\rm If \: the \: sum \: of \: zeroes \: and \: product \: of \: zeroes \: are \: given:-$

$\rm The \: quadratic \: polynomial \: is \: given \: by$

$\rm \orange{ {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes }$

Compare it with x² - 5x - 6

$\rightarrow\rm Sum \: of \: zeroes \: = 5$

$\rightarrow\rm 6 + y = 5$

$\rightarrow\rm y = 5 - 6$

$\rightarrow\rm y = -1$

Let's check the result with product of zeroes

$\rightarrow\rm Product \: of \: zeroes = - 6$

$\rightarrow\rm 6y = - 6$

$\rightarrow\rm y = \dfrac{ - 6}{ \: \: 6}$

$\rightarrow\rm y = - 1$

Hence;

$\boxed{ \sf \purple{ \therefore \: The \: other \: zero \: of \: the \: polynomial \: = - 1}}$