Question

2. Find a quadratic polynomial when sum and product of its zeroes is equal to 0

and √2 respectively.​

Answer 1

To Find :-

• Quadratic polynomial.

Solution :-

Given,

• Sum of roots (α + β) = 0
• Product of roots (αβ) = √2

As we know that,

Quadratic polynomial ;

⟶ x² - (Sum of roots)x + (Product of roots)

[ Put the values ]

⟶ x² - (0)x + √2

⟶ x² - 0x + √2

⟶ x² + √2

Therefore,

The quadratic polynomial is x² + √2.

For information :-

The quadratic formula to find the solution of the quadratic equation ax² + bx + c = 0 is given by,

$\sf \: x = -b \pm \sqrt{ \dfrac{b {}^{2} - 4ac}{2a} }$

Here,

• a, b, c = Real numbers

• a ≠ 0

• x = Unknown