Question

how we find a quadratic polynomial with roots 1/2,3/2.

Answer 1

If the Roots are 1/2, 1/3.

So we can write X = 1/2 & X = 1/3

So, The equations are

(X - 1/2)(X - 1/3) = 0

X² - ( 1/2 + 1/3 )X + 1/6 = 0

6X² - 5X + 1 =0

Or

You can also choose to write as:

$\alpha = 1 \div 2 \\ \beta = 1 \div 3 \\( x - \alpha )(x - \beta ) = 0 \\ x^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ where \: \alpha = 1 \div 2 \\ and \: \: \beta = 1 \div 3$

(For your question, try yourself)
THANKYOU!!!

Answer 2

Answer:

α=1/2 and β=3/2

sum of the zeroes

1/2+3/2=4/2=2

product of the zeroes

1/2*3/2=3/4

the quadratic polynomial is

x^2-(sum of the zeroes)x+(product of the zeroes)

i.e; x^2-2x+3/4

multiply the equation by 4

i.e; 4x^2-8x+3

Hope this helps

Step-by-step explanation: