Question

Form the quadrant polynomial whose zeroes are 4,√3

Answer 1

AnswEr:

Quadratic Polynomial = x² - (4+√3)x + 4√3

ExplaNation:

Given zeroes :

• 4 and √3

To find :

• Quadratic polynomial

Solution :

Sum of zeroes = 4 + √3

Product of zeroes = 4 × √3 => 4√3

Formula for finding quadratic polynomial:

• x² - Sx + P

Here, S refers to sum of zeroes and P refers to product of zeroes.

Quadratic Polynomial = x² - (4+√3)x + 4√3

$\rule{200}2$

VerificaTion:

We know that,

$\red{\sf{Sum\:of\:zeroes\:=\:\dfrac{-b}{a}}}$

: $\implies$ 4 + √3 = 4 + √3

Also,

$\red{\sf{Product\:of\:zeroes\:=\:\dfrac{c}{a}}}$

: $\implies$ 4√3 = 4√3

Hence verified!

Answer 2

Answer: x² - 4+√3x + 4√3 = 0

Step by step explanation:

Let α & β be the zeroes of the polynomial.

α = 4 and β = √3

The formula to get the equation:

x² - ( sum of roots )x + (product of roots) = 0

Sum of roots = α + β and product = αβ

Here,

α + β = 4 + √3 and αβ = 4 × √3

= x² - (4 + √3)x + 4√3 = 0

.°. x² - 4+√3x + 4√3 = 0

Thus, the quadratic polynomial formed is:

x² - 4+√3x + 4√3 = 0