Question

find a quadratic polynomial the sum and product of whose are minus root 2 and 3 by 2 respectively also find its zeros​

Answer 1

Answer:

$\large{\underline{\boxed{\sf 2x^2 + 2\sqrt{2}x + 3}}}$

Step-by-step explanation:

Given that ;

Sum of roots = -√2

Product of roots = 3/2

Let the zeroes of the quadratic polynomial be α and β.

α + β = -√2

αβ = 3/2

Now, we know that;

The quadratic polynomial is given by-

x² - (α + β)x + αβ

⇒ x² - (-√2)x + $\sf \dfrac{3}{2}$

⇒ x² + √2x + $\sf \dfrac{3}{2}$

⇒ $\sf \dfrac{2x^2 + 2\sqrt{2}x + 3}{2}$ = 0

⇒ 2x² + 2√2x + 3

Hence, the required quadratic polynomial is 2x² + 2√2x + 3

Answer 2

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

To Find :- The  quadratic polynomial.

Quadratic Equation Should be in the form of : ax² + bx + c.

For Finding the quadratic polynomial we use this formula :- k = (x² - (α + β)x + αβ ).

It's Given that :-

Sum of roots ( α + β ) = -√2

Product of roots ( αβ ) = 3/2

Now, Putting this in the formula.

k = (x² - (α + β)x + αβ)

k= [ x² - (-√2)x +[tex]\huge\sf\dfrac{3}{2}]

k = x² + √2x + 3/2

k = 2x² + 2√2x + 3 / 2

Let k = 2.

2 = 2x² + 2√2x + 3 / 2

Hence, the required quadratic polynomial is 2x² + 2√2x + 3