14. Find the quadratic polynomial whose zeros are2/3 and 1 Verify ther

1.	14. Find the quadratic polynomial whose zeros are2/3 and 1 Verify therelation between the coefficients and the zeros of the polynomial.415
Answer» ✪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

14. Find the quadratic polynomial whose zeros are2/3 and 1 Verify therelation between the coefficients and the zeros of the polynomial.415

Answer»

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

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

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

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

Then,

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

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

a=3

b=-5

C=2

☞k(3x²-5x+2)

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

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

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

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