Question

find the sum and product of the zeros of the polynomials X power 2 + x- 12​

Answer 1

$\alpha + \beta = - 1$

$\alpha \beta = -12$

Given :-

P(x) = x² + x -12

To find :-

The sum and products of the zeroes of the polynomial.

Solution:-

Let the zeroes of the polynomial be $\alpha$ and $\beta$.

We have,

a = 1,b = 1 , c = -12

Now,

Sum of zeroes of polynomial:-

$\alpha + \beta = \dfrac{-b}{a}$

Put the given value,

→$\alpha + \beta = \dfrac{-1}{1}$

→$\alpha + \beta = -1$

Products of zeroes of polynomial:-

→$\alpha \beta = \dfrac{c}{a}$

→$\alpha \beta = \dfrac{-12}{1}$

→$\alpha \beta = -12$

hence, sum of zeroes is -1 and product of zeroes is -12.

Answer 2

GIVEN :

Polynomial = x² + x - 12

TO FIND:

Sum and product of zeroes

SOLUTION :

Let the zeroes be α and β

We know that,

Sum of zeroes(α+β) using coefficients = -b/a

Product of zeroes(αβ) using coefficients =c/a

From the above polynomial,

a = 1 b = 1 c = -12

Therefore,

Sum of zeroes (α+β) = -b/a = -(1/1) = -1

Product of zeroes (αβ) = c/a = -12/1 = -12