Question

4) If the product af Zeroes of polynomial
ax² - 6x - 6 is 4, find value of a . Find the
Sum of zeroes of polynomial.​

Answer 1

ANSWER:

Given:

• p(x) = ax² - 6x - 6
• Product of zeroes of p(x) = 4

To Find:

• Value of a
• Sum of zeroes of p(x)

Solution:

$\text{We know that, for a quadratic polynomial, Ax ^2 + Bx + C,}\\\\:\implies\text{Product of zeroes}=\dfrac{\text{Constant}}{\text{Coefficient of x ^2 }}=\dfrac{C}{A}\\\\\text{And, we are given that,}\\\\:\implies\text{Product of zeroes}=4\\\\\text{So,}\\\\:\implies\dfrac{C}{A}=4\\\\\text{Here, C=(-6) and A=a}\\\\:\implies\dfrac{-6}{a}=4\\\\:\implies a=\dfrac{-6\!\!\!/^{\:3}}{4\!\!\!/_{\:2}}\\\\\bf{:\implies a=\dfrac{-3}{2}}\\\\\text{Now, we need to find the sum of zeroes of p(x).}$

$\text{We know that, for a quadratic polynomial, Ax ^2 + Bx + C,}\\\\:\implies\text{Sum of zeroes}=\dfrac{\text{-Coefficient of x}}{\text{Coefficient of x ^2 }}=\dfrac{-B}{A}\\\\\text{Here, B=(-6) and A=(-3/2). So,}\\\\:\implies\text{Sum of zeroes}=\dfrac{-(-6)}{\dfrac{-3}{2}}\\\\:\implies\text{Sum of zeroes}=\dfrac{(6\!\!\!/^{\:2})(2)}{-3\!\!\!/}\\\\:\implies\text{Sum of zeroes}=(-2)(2)\\\\\bf{:\implies\text{\bf{Sum of zeroes}}=-4}\\\\\text{\bf{Hence, value of a = (-3/2) and sum of zeroes is -4}}$

Formulae Used:

• Sum of zeroes = -B/A
• Product of zeroes = C/A

Answer 2

Given :

• The product af Zeroes of polynomial

ax² - 6x - 6 is 4 .

To find :

• The sum of zeroes of polynomial.

Solution :

In the given polynomial,

ax² - 6x - 6

a = ?

b = -6

c = -6

Product of zeroes = 4

As we know that,

For a quadratic polynomial

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

$\sf \therefore \frac{c}{a} = 4$

$\sf ⟹ \frac{ - 6}{a} = 4$

$\sf ⟹a = \frac{ - 6}{4} = \frac{ - 3}{2}$

Hence , we got the answer .