Question

let sum of product of zeros of a quadratic polynomial are 5 and 6 respectively then the quadratic polynomial is ​

Answer 1

Answer:

x2-5x+6

Step-by-step explanation:

sum of the zeros(Alpha+beta)=5

product of the Zeroes (alpha×beta)=6

k(x2-(Alpha+beta)+(alpha×beta)

k(x2-5x+6)

x2-5x+6

I hope this answer may help you

Answer 2

$\orange{\mathcal{\underline{\underline{Given:-}}}}$

• Sum Of Zeroes = 5
• Product Of Zeroes = 6

$\orange{\mathcal{\underline{\underline{To \: find:-}}}}$

• Quadratic Polynomial

$\sf \underline{ \blue{ \boxed{ \bf \red{Solution:-}}}}$

$\sf{Let \: \: {\blue{( \alpha \: \: \: and \: \: \: \beta )}\: \: are \: \: the \: zeroes \: of \: the \: Polynomial}}$

Hence,

$\sf{Sum \: of \: zeroes = (\alpha + \beta )}$

$\sf{Product \: of \: zeroes \: = ( \alpha \beta )}$

Formula Used :

$\rm \underline{ \blue{ \boxed{ \bf \green{{x}^{2} - (\alpha + \beta )x + \alpha \beta = 0}}}}$

Putting The Values :

We Get the Polynomial,

$\mathbb\pink{{x}^{2} - 5x + 6 = 0}$

$\tt \underline{ \blue{ \boxed{ \bf \purple{Verification:}}}}$

$\mathcal\pink{{x}^{2} - 5x + 6 = 0}$

$\sf\implies{{x}^{2} -2x - 3x + 6 = 0}$

$\sf\implies{x(x - 2) - 3(x - 2) = 0}$

$\sf\implies{(x - 2) (x - 3) = 0}$

$\sf\blue\implies{\red{x = 2 \: \: \: and \: \: \: 3}}$

Hence,

$\sf{Sum \: Of \: Zeroes=2+3=5}$

$\sf{Product \: Of \: Zeroes=2×3=6}$

$\sf\checkmark{\purple{Verified}}\bigstar$