Question

If one zero of the quadratic polyno-
mial x? - 5x - 6 is 6, then the other
zero is
[C]​

Answer 1

$\rm\huge\blue{\underline{\underline{ Question : }}}$

If one zero of the quadratic polynomial x² - 5x - 6 is 6 then find the other zero.

$\rm\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

Polynomial p(x) = x² - 5x - 6

One of the zero of p(x) is " 6 ".

★ To find,

Another zero of p(x).

★ Let,

According to the general form of the Quadratic Polynomial ax² + bx + c = 0.

a = 1

b = - 5

c = - 6

And one of the zero be

α = 6

$\tt\green{:\implies Sum\:of\;the\:zeroes = \alpha + \beta = \frac{-b}{a}}$

Substitute the values.

$\bf\:\implies 6 + \beta = \frac{-(-5)}{1}⟹6+β= </p><p>1$

$\bf\:\implies 6 + \beta = 5$

$\bf\:\implies \beta = 5 - 6$

$\bf\:\implies \beta = - 1$

$\underline{\boxed{\bf{\purple{ \therefore Another\:zero\:of\:the\:polynomial\:is\:-1.}}}}\:\orange{\bigstar}$

$\begin{gathered}\boxed{\begin{minipage}{7 cm} Some More Information : \\ \\ Sum\:of\:the\:zeroes : \alpha + \beta = \frac{-b}{a}\\ \\ Product\:of\:the\:zeroes : \alpha\beta = \frac{c}{a} \end{minipage}}\end{gathered}$