Question

8. Find a quadratic polynomial whose sum and product of its zeroes are 1\4 and -1 respectively.​

Answer 1

Given:

$\star \bold{ sum \: of \: zeroes = \frac{1}{4} } \\ \\ \star \bold{product \: of \: zeroes \: = - 1}$

To find :

$\star \bold{quadratic \: polynomial}$

Solution:

As we know that :

$\star \boxed{\bold{ quadratic \: polynomial = {x}^{2} - (sum)x + (product)}}$

Put the given values:

$\implies \: f(x) = {x}^{2} - ( \frac{1}{4} )x + ( - 1) = 0 \\ \\ \implies \: f(x) = {x}^{2} - \frac{1}{4} x - 1 = 0 \\ \\ \implies \: f(x) = \frac{4 {x}^{2} - x - 4}{4} = 0 \\ \\ \implies \: f(x) = 4 {x}^{2} - x - 4 = 0$

Hence, the quadratic polynomial is :

• 4x²-x-4= 0

Answer 2

Question:-

Find a quadratic polynomial whose sum and product of its zeroes are 1\4 and -1 respectively.

To Find:-

Quadratic polynomial

Solution:-

➭ 4x² - x - 4 = 0

Formula :-

Quadratic polynomial = x² - (sum) x + product

=> substitute with the given values

➭ f ( x ) = x² - (1/4)x + [-1] = 0

➭ f ( x ) = x² - x/4 - 1 = 0

➭ f ( x ) = 4x² - x - 4 = 0

4

➭ f( x ) = 4x² - x - 4 = 0(4)

➭ f( x ) = 4x² - x - 4 = 0

★ Quadratic equation

= 4x² - x - 4 = 0

☞ Hence verified