Question

Find a quadratic polynomial, the sum and product of whose zeroes are 0 and - root 2 respectively

Answer 1

sum of the root = 0
product of the root  = -√2
Equation for a quadratic polynomial
x^2+(sum of the root)x+(product of the root) = 0
x^2 + 0 x -√2 = 0
x^2 - √2 = 0

Answer 2

Answer:

Step-by-step explanation:

Concept:

A degree two polynomial is a quadratic polynomial.

A polynomial of degree two, or one in which two is the highest exponent of the variable, is a quadratic polynomial. A quadratic polynomial will typically take the following form:  P(x) = ax2 + bx + c, $a$ ≠ $0$

When we convert a quadratic polynomial to a constant, we have a quadratic equation.

Any equation written as p(x)=c, where p(x) is a polynomial of degree 2 and c is a constant, is referred to as a quadratic equation.

Given:

The sum of the roots is  $0$ and the product of the roots is $-\sqrt{2}$

Find: To find a quadratic polynomial

Solution:

Given the  sum of the roots $\alpha +\beta = 0$

and Product of the roots $\alpha \beta = -\sqrt{2}$

∴ Quadratic polynomial = $x^{2} - (\alpha +\beta ) + \alpha \beta$

                                         $x^{2} - (0)x + (-\sqrt{2} )$

                                         $x^{2} - 0- \sqrt{2}$

                                         $x^{2} - \sqrt{2}$

Hence the quadratic polynomial is $x^{2} - \sqrt{2}$

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