Question

if the sum and the product of zeros of the polynomial ax²-6x-c is equal to 12 find the values of a and c ​

Answer 1

$\huge{\mathcal{\green{\underline{Answer}}}}$

Let alpha and beta are the zeroes of the above polynomial

Sum of the zeroes :

$\alpha + \beta = 12 \\ = \frac{ - b}{a}$

b=-6

a'=a

$12 = \frac{ - ( - 6)}{a} \\ a = \frac{6}{12}$

$\large{\implies{\purple{a=1/2}}}$

Product of the zeroes :

$\alpha \beta = 12 = \frac{c}{a}$

C=-c

a=1/2

$12 = \frac{ - c}{1 \div 2} \\ 12 = - 2c$

$\large{\implies{\purple{c=6}}}$

Answer 2

SOLUTION:-

Given:

If the sum & the product of zeroes of the polynomial ax² -6x -c is equal to 12.

To find:

The value of a & c.

Explanation:

Sum of zeroes in quadratic polynomial:

$\alpha + \beta = \frac{ - b}{a} = \frac{ - Coefficien t \: of \: x}{Coefficient \: of \: {x}^{2} }$

We have,

ax² -6x -c

$\alpha + \beta = - \frac{( - 6)}{a} \\ \\ \frac{6}{a} = 12 \\ \\ 12a = 6 \\ \\ a = \frac{6}{12} \\ \\ a = \frac{1}{2}$

&

Product of zeroes in quadratic polynomial:

$\alpha \beta = \frac{c}{a} = \frac{Constant \: term}{Coefficient \: of \: {x}^{2} }$

Therefore,

Putting the value of a in product of zeroes;

$\frac{c}{a} = 12 \\ \\ 12a = c \\ \\ 12 \times \frac{1}{2} = c \\ \\ \frac{12}{2} = c \\ \\ 6 = c$

Thus,

The value of a = 1/2 &

The value of c= 6.