Question

find a quadratic polynomial whose sum and product of the zeros are √2 , -3/2​

Answer 1

Answer:

x²-(sum) x + product

x²-√2x-3/2

OR

2x²-2√2x-3

hope it helps

Answer 2

Given : The sum and product of zeroes are √2 and – 3/2 , respectively.

Need To Find : The Quadratic Polynomial ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀ ✇ We've provided with the sum and product of zeroes of Polynomial . By Using , the Formula of Quadratic Polynomial we'll find Polynomial .

》 Formula for Quadratic Polynomial is Given by :

⠀⠀⠀⠀⠀⠀➟   x² – { α + β } x + { α β }

Where ,

• Sum of Zeroes : { α + β } = √2 &
• Product of Zeroes : { α β } = – 3/2 .

⠀⠀⠀⠀⠀⠀⠀★ By Substituting the Given Values in Formula :

⇢ x² – { α + β } x + { α β }

⇢ x² – { √2 } x + { - 3/2 }

⇢ x² – √2 x – 3/2

⇢ 2x² – 2√2 – 3

⇢ 2x² – 2√2x – 3 ★

⠀⠀⠀⠀⠀⠀∴ Hence , Quadratic Polynomial is 2x² – 2√2x – 3 .