Question

Write a quadratic polynomial whose zeros are root 2 and minus root 2

Answer 1

Answer:

alpa= √2. beta= -√2

Q= x²- (alpa+beta)x + alpa(beta)

=X²- (√2-√2)x + √2(-√2)

= x²- 0x - 2

= x²- 2

I hope it will help you

Answer 2

AnsWer :

X²- 2.

Given :

• General equation ax²+bx+c=0, a not equal to 0.
• It's two zeros √2 and -√2.

Concepts Required :

$\blacksquare \tt Sum \: of \: zero. \\ \tt \alpha + \beta = \frac{ - b}{a} = \frac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$

$\blacksquare\tt Product \: of \: zero\\ \tt\alpha \beta = \frac{c}{a} = \frac{constant \: term}{coefficient \: of \: {x}^{2} }$

Solution :

Let two zeros be alpha and beta.

$\tt\alpha = \sqrt{2} \: \: \: and \: \: \: \beta = -\sqrt{2}.$

We have formula,

$\tt k( {x}^{2} - sx + p)$

• k Constant term.
• S Sum of zeros.
• P product of zeros.

Putting value, given above.

$\tt k( {x}^{2} - (\sqrt{2 }-\sqrt{2})x + (\sqrt{2} \times -\sqrt{ 2}))$

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

$\tt k ({x}^{2} - 2).$

Let's Verify :

We have equation,

$\tt\implies {x}^{2} - 2 = 0.$

$\tt \implies{x}^{2} = 2.$

$\tt\implies x = \pm\sqrt{2}.$

Therefore, our Equation should be x²-2.