Question

Find the zeros of p(x)= x³-x and hence verify the relationship between zeros and coefficients

Answer 1

Answer:

x3-x=0

then, x3=x

SO NOW

THERE ARE 3ZEROS

THERE ARE ONE COEFFICIENT

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Answer 2

✪AnSwEr

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

• A polynomial
• X²-X

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

• Factors of the polynomial
• Relationship between cofficient

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

X²-X

=>X²-X

=>X(X-1)

=>X=1,0

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=-1
• C=0

☞

________________________________

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{1}{1}$

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

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{0}{1}$

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

________________________________

Hence,relation verified