Question

form a quadratic polynomial whose zeroes are 1/2 and 2/3

Answer 1

Answer:

$\large\green{\textsf{✩ Verified Answer ✓ }}$

_______________...❀♡❀...________________

$\large\pink{\textsf{Refer The Attachment ..}}$

_______________...❀♡❀...________________

$\bf\orange{\textsf{Answered By ❥ MrAkdu࿐ }}$

Answer 2

Answer:

A quadratic polynomial whose zeroes are -\frac{1}{2}−

2

1

and \frac{2}{3}

3

2

is x^2-x-2=0x

2

−x−2=0

Step-by-step explanation:

To find : A quadratic polynomial whose zeroes are -\frac{1}{2}−

2

1

and \frac{2}{3}

3

2

?

Solution :

The roots of the quadratic equation ax^2+bx+c=0ax

2

+bx+c=0 are \alphaα and \betaβ .

So, Let \alpha=-\frac{1}{2}α=−

2

1

and \beta=\frac{2}{3}β=

3

2

The formula to get the equation is

x^2-(\alpha+\beta)x+\alpha\beta=0x

2

−(α+β)x+αβ=0

Substitute the values,

x^2-(-\frac{1}{2}+\frac{2}{3})x+(-\frac{1}{2})(\frac{2}{3})=0x

2

−(−

2

1

+

3

2

)x+(−

2

1

)(

3

2

)=0

x^2-\frac{1}{6}x-\frac{1}{3}=0x

2

−

6

1

x−

3

1

=0

x^2-x-2=0x

2

−x−2=0

Therefore, a quadratic polynomial whose zeroes are -\frac{1}{2}−

2

1

and \frac{2}{3}

3

2

is x^2-x-2=0x

2

−x−2=0