Question

find a quadratic polynomial, the sum and the product or zeroes are root 2 and-3/2 respectively. also find it's zeroes​

Answer 1

Answer:

Sum of zeroes and Product of zeroes are respectively:

$\alpha = - b \div a \\ \beta = c \div a \: \: \:$

So we have given

$\alpha = 2$

So

$\alpha = 2 \div 1 = - b \div a$

So, 2/1 = -b/a

b = -2 and a = 1

Now,

$\beta = - 3 \div 2 = c \div a$

So, -3/2 = c/a

c = -3 and a =2

But we have find a = 1 in above...

So to make a = 2 we'll multiply a=1 by 2

So, if we are multiplying denominator by 2 we have to divide numerator also by 2...

So we get b= -2*2 and a=1*2

b= -4 , a=2 , c= -3

So required quadratic polynomial is

Standard form of quadratic polynomial is....

ax^2+bx+c

Now replace the values of a,b and c

We get------> 2x^2-4x-3