Question

find the quadratic polynomial whose zeroes are 1/2 and 1​

Answer 1

Answer:

2x^2-x+2

Step-by-step explanation:

let a+b=1/2

& a×b=1

now,

x^2-(sum of zeros)x+product

x^2-(a+b)x+a×b

×2-1/2x+1

by taking LCM

2X^2-x+2

Answer 2

The quadratic polynomial whose zeroes are $\dfrac{1}{2}$  and 1​ is $x^2$ - ($\dfrac{3}{2}$)x + $\dfrac{1}{2}$.

Step-by-step explanation:

Let α and β be the roots of  are zeroes.

Here, α = $\dfrac{1}{2}$ and β = 1

To find, the quadratic polynomial whose zeroes are $\dfrac{1}{2}$  and 1​ = ?

We know that,

The equation of quadratic polynomial:

$x^2$ - (sum of zeros)x + Product  of zeroes

= $x^2$ - (α + β)x + αβ

= $x^2$ - ($\dfrac{1}{2}$  + 1)x + $\dfrac{1}{2}$ . 1

= $x^2$ - ($\dfrac{3}{2}$)x + $\dfrac{1}{2}$

Thus, the quadratic polynomial whose zeroes are $\dfrac{1}{2}$  and 1​ is $x^2$ - ($\dfrac{3}{2}$)x + $\dfrac{1}{2}$.