Question

If the product of the zeroes of ax2

-6x -6 is 4. Find the value of a. Hence

find the sum of its zeroes.

Answer 1

Solution -

We have a quadratic polynomial,

• ax² - 6x - 6

It is given that, product of zeroes of the given polynomial is 4.

⠀

We know that,

➝ αβ = $\sf{\dfrac{c}{a}}$

⠀

Here,

• c = -6
• a = a

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By putting the values

$\tt\dashrightarrow{\dfrac{-6}{a} = 4}$

⠀

$\tt\dashrightarrow{-6 = 4a}$

⠀

$\tt\dashrightarrow{a = \dfrac{-6}{4}}$

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$\tt\dashrightarrow{a = \dfrac{-3}{2}}$

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Therefore,

• Value of a is -3/2.

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Now, we have to find the sum of zeroes of the given polynomial. We know that,

➝ α + β = $\sf{\dfrac{-b}{a}}$

⠀

Calculation

$\tt\dashrightarrow{\alpha + \beta = -(-6) \times \dfrac{2}{-3}}$

⠀

$\tt\dashrightarrow{\alpha + \beta = 6 \times - \dfrac{2}{3}}$

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$\tt\dashrightarrow{\alpha + \beta = 2 \times (-2)}$

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$\frak\dashrightarrow{\purple{\alpha + \beta = -4}}$

⠀

★ $\small\underline{\sf{Hence,\: sum\: of\: zeroes\: is\: -4.}}$

Answer 2

A N S W E R :

• Sum of zeroes is -4.

Given :

• ax² - 6x - 6

To find :

• Find sum of zeroes ?

Solution :

• Comparing it to ax² + bx + c

=> a = a

=> b = -6

=> c = -6

=> Product of zeroes = c/α

=> Product of zeroes = -6/α

Also,

• Given that products of zeroes = 4

Therefore,

• 4 = -6/α

=> 4a = -6

=> a = -6/4

=> a = -3/2

Now, Substituting the values,

• Given Polynomial

=> -3/2x² - 6x - 6 = 0

• Taking L.C.M

=> -3x² - 12x - 12 = 0

• Taking 3 as common

=> -x² - 4x - 4 = 0

• Sum of zeroes = -β/α

=> Sum of zeroes = -(-4)/-1

=> Sum of zeroes = -4

Hence,

• Sum of zeroes is -4.