Question

find the quadratic polynomial the sum and product of whose zeroes are √2 and -3/2 respectively also find its zeros

Answer 1

Step-by-step explanation:

Sum of zeroes = √2

product of zeroes = -3/2

The quadratic equation will be in the form of :

x²- Sx + P

Hence,

x² - √2x - 3/2

______________________________

Firstly, we have to take lcm of the complete equation.

The equation will be :

2x² - 2√2x² - 3 = 0

By using quadratic formula,

x = (- b ± √D)/2a

Where, D = b²- 4ac

= (-2√2)²-4(2)(-3)

=8+24

=32

Now, put the value of D in above formula. we get,

x = (2√2 ± √32)/(2×2)

x = (2√2±√32)/4

x = (2√2+√32)/4. and x = (2√2 - √32 )/ 4

Answer 2

$\huge\pink{\mathfrak{answer}}$

Quadratic polynomial with α,β as zeroes would be (x−α)(x−β);

Here, the polynomial would be (x+2)(x+6)=x² +8x+12