Question

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.
(i) xsquare -2x-8

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• A polynomial

• X²-2x-8

${\sf{\green{\underline{\large{To\:Find}}}}}$

• Factors of the polynomial

• Relationship between cofficient

${\sf{\pink{\underline{\Large{Explanation}}}}}$

X²-2x-8

we have to spilt the middle term in such a way that the product become -8 and sum become -2

X²-2x-8

=>X²-4x+2x-8

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

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

=>x=-2,4

Let the zeroes of the polynomial be$\tt\alpha{and}\beta$

Then,

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

&

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

Here,

a=1

b=-2

C=-8

☞

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{-(-2)}{1}$

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{Cofficient\:of\:X}{Cofficient\:of\:x^2}=$

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{-8}{1}$

$\rightarrow\tt{\large\alpha{\times}\beta{=}\dfrac{Constant\:term}{Cofficient\:of\:x^2}}$

Hence,relation verified

Answer 2

Answer:

Step-by-step explanation:

Heyy..!

Refer attachment ^_^