Question

The sum and product respectively of zeroes of the polynomial x2-4x+3 are

Answer 1

Given :

• Polynomial x²-4x+3.

To Find :

• Sum and Product of the Zeroes.

Solution :

$\longmapsto\tt\bold{{x}^{2}-4x+3}$

By Splitting Middle Term :

$\longmapsto\tt{{x}^{2}-(3x+1x)+3}$

$\longmapsto\tt{{x}^{2}-3x-1+3}$

$\longmapsto\tt{x(x-3)-1(x-3)}$

$\longmapsto\tt{(x-1)(x-3)}$

• x = 1
• x = 3

So , 1 and 3 are the zeroes of polynomial x²-4x+3...

_______________________

Here :

• a = 1
• b = -4
• c = 3

Sum of Zeroes :

$\longmapsto\tt{\alpha+\beta=\dfrac{(-b)}{a}}$

$\longmapsto\tt{1+3=\dfrac{-(-4)}{1}}$

$\longmapsto\tt\bold{4=4}$

Product of Zeroes :

$\longmapsto\tt{\alpha\beta=\dfrac{c}{a}}$

$\longmapsto\tt{1\times{3}=\dfrac{3}{1}}$

$\longmapsto\tt\bold{3=3}$

HENCE VERIFIED

Answer 2

Given:-

★ x² - 4x + 3 is a polynomial.

To find:-

★Sum and the product of the given polynomial

Solution:-

x² - 4x + 3

By doing middle term factorisation,

= x² - (3 + 1)x + 3

= x² - 3x - x + 3

= x (x-3) - 1 (x -3)

= (x-3) (x-1).

now, x² - 4x + 3 = 0

➟ ( x-3) (x-1) = 0

➟ (x-3) = 0 and (x-1) = 0

➟ x = 3 and x = 1.

➬α = 3 and β = 1.

So,

Sum of zeroes = α + β = 3 + 1 = 4.

And

Product of Zeroes = αβ = 3 × 1 = 3.

$\underline{\mathtt{Here\:is\:Your\:Answer}}$

${\boxed{\huge{\underline{\mathtt{\red{Thank\:You}}}}}}$