Question

Find a quadratic polynomial with 1/2 and 1/3 as the sum and product of its zeroes respectively.

please give full explanation clearly

​

Answer 1

Answer:

i) 41, -1

Using the quadratic equation formula,

x2−(Sum  of  root)x+(Product  of  root)=0

Substitute the value in the formula, we get

x2−41x−1=0

4x2−x−4=0

(ii) 2,31

Using the quadratic equation formula,

x2−(Sum  of  root)x+(Product  of  root)=0

Substitute the value in the formula, we get

x2−2x+31=0

Multiply by 3 to remove denominator, 

3x2−32x+1=0

(iii) 0, 5

Using the quadratic equation formula,

x2−(Sum  of  root)x+(Product  of  root)=0

Substitute the value in the formula, we get

x2−0x+5=0

x2+5

Answer 2

Answer:

x²-1/2x+1/3

Step-by-step explanation:

Given⤵

➡Sum of zeros = 1/2

➡Product of zeros = 1/3

To find⤵

➡Quadratic polynomial

Solution⤵

⚫Using formula X²- (Sum of zeros)x +Product of zeros , we get

$➡{x}^{2} - ( \frac{1}{2} )x + \frac{1}{3}$

$✅Hence, \: the \: quadratic \: polynomial \\ is \: \: \: {x}^{2} - \frac{1}{2} x + \frac{1}{3} .$

✔Extra points⤵

✡If sum and product of zeros are given and a quadratic polynomial then we put the sum of zeros and product of zeros in formula..

x²-(sum of zeros) x ( product of zeros).

Hope this is helpful to you!