Question

find the zeros of the quadratic polynomial and verify the relationship between the zeros and the coefficients.

x²-2x-8

Answer 1

Step-by-step explanation:

The first term is,  x^2  its coefficient is  1 .

The middle term is,  -2x  its coefficient is  -2 .

The last term, "the constant", is  -8 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -8 = -8 

Step-2 : Find two factors of  -8  whose sum equals the coefficient of the middle term, which is   -2 .

-4   +   2   =   -2   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  2 

                   

 x^2 - 4x + 2x - 8.

x(x-4)2(x-4)=0.

(x+2)(x-4)=0

x+2 = 0 (or) x-4=0.

x= -2 or x= 4.

Relationship between zeroes and the coefficients of the polynomial.

α+β = -b/a.

αβ =c/a.

Sum of zeroes and its relationship with coefficients.

α+β = -b/a.

=》-2+4 =-(-2)/1

=》2=2/1

=》2=2.

Product of zeroes and its relationship with coefficients.

αβ =c/a.

(-2)(4)=-8/1

-8=-8.

Answer 2

HEre Is Your Ans ⤵

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➡X² - 2X - 8 = 0

➡X² - 4X + 2X - 8 = 0

➡X(X - 4) + 2(X - 4) = 0

➡(X + 2)(X-4) = 0

➡X = -2 Or X = 4

Here ,

α = - 2

β = 4

a = 1

b = - 2

c = - 8

Verification :-

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

$= > - 2 + 4 = \frac{ - (- 2)}{1} \\ \\ = > 2 = 2$

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

$= > - 2 \times 4 = \frac{ - 8}{1} \\ \\ = > - 8 = - 8$

Hence , Verified

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