Question

14. Find the quadratic polynomial whose zeros are
2/3 and 1 Verify the
relation between the coefficients and the zeros of the polynomial.
4
15​

Answer 1

✪AnSwEr

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

• Zeroes of polynomial is 2/3 and 1

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

• Relationship between coefficient and zeroes
• Finding quadratic polynomial

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

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

Then,

$\tt\alpha{+}\beta=\dfrac{-b}{a}{=}\dfrac{2}{3}+1=\frac{5}{3}$

&

$\tt\alpha{\times}\beta{=}\frac{c}{a}=\frac{2}{3}\times{1}=\frac{2}{3}$

Here,we conclude that

a=3

b=-5

C=2

Now creating the quadratic polynomial

☞k(3x²-5x+2)

Coefficient Relationship

$\tt\alpha{+}\beta=\dfrac{-b}{a}{=}\dfrac{2}{3}+1=\frac{5}{3}$

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

&

$\tt\alpha{\times}\beta{=}\frac{c}{a}=\frac{2}{3}\times{1}=\frac{2}{3}$

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

Hence,relation verified