Question

if the polynomial of zeroes of ax²-6x-6 is 4 find
a) find a
b) also find the sum of zeroes ​

Answer 1

$\dag\:\underline{\sf AnsWer :}$

Here we are given a polynomial p(x) = ax² - 6x - 6 and product of zeroes is 4. First compare the given polynomial with our general equation ax² + bx + c = 0. On comparing we have observed that a = a , b = -6 , c = -6. In the question it is mentioned that we have to find the value of a and also we have to find the sum of zeroes.

• Before going to solve this question we should know the following things :

$\bullet\:\sf Sum \: of \: zeroes = \dfrac{-b}{a}$

$\bullet\:\sf Product \: of \: zeroes = \dfrac{c}{a}$

$\bigstar\:\underline{\textbf{According to the Question Now :}}$

$:\implies\sf Product \: of \: zeroes = \dfrac{c}{a}$

$:\implies\sf\dfrac{c}{a} = 4$

$:\implies\sf \dfrac{ - 6}{a} = 4$

$:\implies\sf \dfrac{ - 6}{4} = a$

$:\implies \underline{ \boxed{\sf a = \dfrac{ - 3}{2}}}$

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$\longrightarrow\:\:\sf Sum \: of \: zeroes = \dfrac{-b}{a}$

$\longrightarrow\:\:\sf Sum \: of \: zeroes = \dfrac{ - (-6)}{ \dfrac{ - 3}{2} }$

$\longrightarrow\:\:\sf Sum \: of \: zeroes = \dfrac{6}{ \dfrac{ - 3}{2} }$

$\longrightarrow\:\:\sf Sum \: of \: zeroes = 6 \times \dfrac{ 2}{ - 3}$

$\longrightarrow\:\:\sf Sum \: of \: zeroes = \dfrac{ 12}{ - 3}$

$\longrightarrow\:\: \underline{ \boxed{\sf Sum \: of \: zeroes = - 4}}$

Answer 2

Correct Question-:

• If the products of zeroes of the polynomial ax²-6x-6 is 4 .
• a) Find a
• b) Also find the sum of zeroes .

AnswEr-:

• $\boxed{\sf{\large { a = \:\dfrac{-3}{2}\:}}}$
• $\boxed{\sf{\large { \:Sum \:of\:it's\:zeroes=\:(-4)\:}}}$

EXPLANATION-:

• $\dag{\sf{\large {Given-:}}}$

• Polynomial-: p(x) = ax²-6x-6
• The Sum of it zeroes is -: 4

• $\dag{\sf{\large {To\:Find-:}}}$

• Find a .
• Find the sum of it's zeroes.

$\dag{\sf{\large {Solution:}}}$

• $\dag{\sf{\large {First-:}}}$

• Compare p(x) = ax²-6x-6 this polynomial to general equation ax² + bx + c = 0

• On comparing,

• We have got -:
• a = a
• b = -6
• c = -6

◇ As We know that ,

• $\star{\sf{\large {Sum\:of\:it\:zeroes\:= \:\dfrac{-b}{a}\:or\:\dfrac{-(Cofficient\:of\:x)}{Cofficient\:ofx^{2}}}}}$

• $\star{\sf{\large {Product\:of\:it\:zeroes\:= \:\dfrac{c}{a}\:or\:\dfrac{(Constant\:term)}{Cofficient\:ofx^{2}}}}}$

Now ,

• $\dag{\sf{\large {Product\:of\:it\:zeroes\:= \:\dfrac{c}{a}\:or\:\dfrac{(Constant\:term)}{Cofficient\:ofx^{2}}}}}$

• Here -:
• c = (-6) = Constant term
• a = a = Cofficient of x²
• Product of zeroes = 4

• $\implies{\sf{\large {Product\:of\:it\:zeroes\:= \:\dfrac{-6}{a}\:=4}}}$

• $\implies{\sf{\large { \:\dfrac{-6}{a}\:=4}}}$

• $\implies{\sf{\large { a=\:\dfrac{-6}{4}\:}}}$

• $\implies{\sf{\large { \:\dfrac{-3}{2}\:=a}}}$

$\dag{\sf{\large {Therefore:}}}$

• $\boxed{\sf{\large { a = \:\dfrac{-3}{2}\:}}}$

Now ,

• $\star{\sf{\large {Sum\:of\:it\:zeroes\:= \:\dfrac{-b}{a}\:or\:\dfrac{-(Cofficient\:of\:x)}{Cofficient\:ofx^{2}}}}}$

• Here -:
• b = -6

• $\implies{\sf{\large { a\:= \dfrac{-3}{2}\:}}}$

• $\implies{\sf{\large {Sum\:of\:it\:zeroes\:= \:\dfrac{-(-6)}{\frac{-3}{2}}\:}}}$

• $\implies{\sf{\large { \:\dfrac{-(-6)}{\frac{-3}{2}}\:}}}$

• $\implies{\sf{\large { \:\dfrac{6}{\frac{-3}{2}}\:}}}$

• $\implies{\sf{\large { \: 6 \times \dfrac{-2}{3}\:}}}$

• $\implies{\sf{\large { \:2 \times (-2)\:}}}$

• $\implies{\sf{\large { \:Sum \:of\:it's\:zeroes=\:(-4)\:}}}$

Therefore,

• $\boxed{\sf{\large { \:Sum \:of\:it's\:zeroes=\:(-4)\:}}}$

HENCE -:

• $\boxed{\sf{\large { a = \:\dfrac{-3}{2}\:}}}$

• $\boxed{\sf{\large { \:Sum \:of\:it's\:zeroes=\:(-4)\:}}}$

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