Question

Find the sum of the zero of the
quadratic
polynomiay x²+7x+12​

Answer 1

Answer:

Given:- The polynomial is x² + 7x + 12

To find : The sum and product of zeroes of the polynomial.

solution:-

First of all we have to find out the zeroes of the p(x).

here ,

⇒ a = 1

⇒b = 7

⇒c = 12

⇒p( x ) = x² + 7x + 12

⇒p ( x ) = 0

⇒ x² + 7x + 12 = 0

⇒ x² + ( 4 + 3 ) x + 12 =0

⇒x² + 4x + 3x + 12 = 0

⇒x ( x + 4 ) + 3 ( x + 4 ) = 0

⇒( x + 4 ) ( x + 3 ) = 0

so , Either

↦( x + 4 ) = 0

↦ x = -4

or,

↦( x + 3 ) = 0

↦x = -3

. • . The zeroes are -4 , -3

Now ,

let, the Zeroes be α ,β

so, α = -4 , β = -3

$\therefore{Sum \:Of \:the \:Zeroes(α+β)}$

= -4 + ( -3)

= -4 -3

= -7

= $\frac{-7 }{1}$

= -7

= $\frac{-b}{a}$

= $\frac{- Coefficient \:Of \:x}{Coefficient \:Of \:x²}$

$\therefore{product \:of \:the \:zeroes(αβ)}$

= -4 × -3

= 12

= $\frac{12}{1}$

= 12

= $\frac{c}{a}$

= $\frac{Constant \:term}{Coefficient \:Of \:x}$

★Note:

★ For quadratic Equation Or polynomial-

☆ Formulla to find the sum of zeroes is

= -Coefficient of x / coefficient of x²

= - b / a

☆ Formulla to find the product of zeroes

= constant term / coefficient of x

= c / a

Answer 2

Answer:

Step-by-step explanation:

Let f(x)=$x^{2} +7x+12$

$x^{2} +3x+4x+12$                                   {12=3*4}

                                                               {7=3+4}

$(x^{2} +3x)+(4x+12)\\x(x+3) +4 (x+3)\\(x+3) (x+4)\\either ,\\x+3=0 \\x=-3\\x+4=0\\x=-4$

zeros = -3, -4

α= -3 ,β= -4

f(x)=$x^{2} +7x+12$

   =  $1x^{2} +7x+12$

comparing with $ax^{2}+bx+c$

so , a=1 , b=7 , c=12

now finding sum of zeros

Sum of zero = $\frac{-b}{a}$

α +β = $\frac{-b}{a}$

-3+(-4)=$\frac{-7}{1}$

-7=-7

product of zeros =  $\frac{c}{a}$

α*β=$\frac{c}{a}$

(-3)(-4)=$\frac{12}{1}$

12=12

Hope it will help you

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