Question

find the quadratic polynomial in each case with the given numbers as the sum and product of its zeros respectively (i) 1/4,_1 ii) 0,root5 iii) 1,1 iv) -1/3,1/4 v 4,1​

Answer 1

Answer :

$\bf (i)x^{2} -\frac{x}{4} -1 \\\\ (ii) x^{2} +\sqrt{5} \\\\ (iii)x^2-x+1 \\\\ (iv) x^{2} +\frac{x}{3} +\frac{1}{4} \\\\ (v) x^{2} -4x+1$

Step-by-step explanation :

When the sum and product of zeroes are given,

the quadratic polynomial is of the form :

x² - (sum of zeroes)x + (product of zeroes)

$\bf (i) \frac{1}{4} , -1$

 Sum of zeroes = 1/4

 Product of zeroes = -1

The required quadratic polynomial is

   $\implies x^{2} -(\frac{1}{4})x+(-1) \\\\ \bf \implies x^{2} -\frac{x}{4} -1$

$\bf (ii) 0,\sqrt{5}$

  Sum of zeroes = 0

  Product of zeroes = √5

The required quadratic polynomial is

 $\implies x^{2} -(0)x+(\sqrt{5}) \\\\ \implies x^2-0+\sqrt{5} \\\\ \bf \implies x^{2} +\sqrt{5}$

$\bf (iii)1,1$

   Sum of zeroes = 1

   Product of zeroes = 1

The required quadratic polynomial is

  $\implies x^2-(1)x+1 \\\\ \bf \implies x^2-x+1$

$\bf (iv) \frac{-1}{3},\frac{1}{4}$

  Sum of zeroes = -1/3

  Product of zeroes = 1/4

The required quadratic polynomial is

 $\implies x^{2} -(\frac{-1}{3})x+(\frac{1}{4}) \\\\ \implies \bf x^2+\frac{x}{3}+\frac{1}{4}$

$\bf (v) 4,1$

  Sum of zeroes = 4

  Product of zeroes = 1

The required quadratic polynomial is

  $\implies x^2-(4)x+1 \\\\ \bf \implies x^2-4x+1$

Answer 2

Step by step explanation