Question

what is the quadratic polynomial whose sum and the product of zeroes is root2, 1/2 respectively​

Answer 1

Answer:

FINDING POLYNOMIAL USING FORMULA-x²-(sum of zeroes)x+product of zeroes

=x²-root2x+1/2

=2x²-root2x+1. (takin 2 out of bracket)

Step-by-step explanation:

polynomial is 2x²-root2x+1

HOPE THIS WILL HELP YOU!

Answer 2

☯GIVEN :

• $\alpha + \beta = \sqrt{2}$ and $\alpha \beta = \dfrac{1}{2}$ .

☯TO FIND :

• Quadratic Polynomial.

☯FORMULA REQUIRED :

• $\underline{\boxed{\purple{\bf{x^2- \left(\alpha + \beta\right)x + \alpha\beta =0 }}}}$

➲SOLUTION :

We have,

• By substituting the values, $\alpha + \beta = \sqrt{2}$ and $\alpha \beta = \dfrac{1}{2}$ :

$:\implies {\sf x^2 - \left(\alpha + \beta \right)x + \alpha \beta = 0}$

$:\implies {\sf x^2- (\sqrt{2} )x+\dfrac{1}{2} =0 }$

$:\implies {\sf x^2- \sqrt{2} x+\dfrac{1}{2 } =0 }$

$:\implies {\sf \dfrac{2 x^2 - 2\sqrt{2} x + 1}{2} =0 }$

• By cross multiplication :

$:\implies {\sf 2 x^2 - 2\sqrt{2} x + 1 = 0 \times 2}$

$:\implies{ \underline{ \boxed{ \blue{\bf{ 2 x^2 - 2\sqrt{2} x + 1 = 0}}}}}$

$\huge{\green{\therefore}}$ Quadratic Polynomial = $\bf{ 2 x^2 - 2\sqrt{2} x + 1 }$.