Question

prepare a quadratic equation whose roots are 1÷2;1÷2

Answer 1

$two \: roots \: \: are \: (\frac{1}{2}) and \: ( \frac{1}{2} ) \\ the \: formula \: for \: quadratic \: eqn \: is \: k {x}^{2} - ( \alpha + \beta ) \: + ( \alpha \beta ) \\ ie \: {x}^{2} - \frac{1}{2} + \frac{1}{2} \\ {2x}^{2} - 1 + 1 \\ is \: the \: required \: eqn$

Answer 2

Answer:

The quadratic polynomial is  4x² - 4x + 1

Step-by-step explanation:

Given ::- roots are 1/2 and 1/2

Solution::-

Let roots be α and β

So, α + β = 1/2 + 1/2

= 1+1 /2

= 2/2

= 1

αβ = 1/2 × 1/2

= 1/4

The general formula for quadratic equation is ::-

x² - (α + β)x + (αβ)

= x² - (1)x + (1/4)

= x² - x + 1/4

Multiplying the equation with 4

= 4x² - 4x + 1

This is the required quadratic polynomial

HOPE IT HELPS YOU!!