Question

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

Answer 1

x^2 - 5x - 6

= x^2 -6x + x - 6

= x(x-6) +1(x-6)

= (x-6)(x+1)

For zeros of the polynomial (x-6)(x+1) must be equal to zero.

That is,

(x-6)(x+1) = 0

=> x-6=0 or x+1=0

x = 6 or x = -1

Hence, the other zero of the given polynomial is x = -1.

Answer 2

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

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.

$\bf\:\implies 6 + \beta = \frac{-(-5)}{1}$

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

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

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

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

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