Question

find the quadratic equation whose zeroes are -√2 and √2​

Answer 1

Answer:

x² - 2 is the quadratic equation.

Step-by-step explanation:

Given :-

Zeroes are -√2 and √2​.

To find :-

Quadratic equation.

Solution :-

Sum of zeroes = -√2 + √2 = 0

Product of zeroes = -√2 × √2 = -√4 = -2

Quadratic polynomial general form:-

x² - (α+β)x + α×β)

So, we get :-

x² - (0)x + (-2)

∴ x² - 2 is the quadratic equation.

Answer 2

Topic

Quadratic equation

Solution

♦ Zeros = -√2 and √2

$\sf{Sum \: of \: zeros \: (α+β)= -√2 + √2 =0}$

$\sf{Product \: of \: zeros \: (α×β) = -√2 × √2 = -2}$

Quadratic equation in the form of roots:

$\pink{x² – (α+β)x + (αβ) = 0}$

Substitute the values

$\sf{ \implies \: x²-0x+(-2)} \\ \\ \sf{ \implies \red{x²-2}}$

So the required quadratic equation is x²-2

--------------------------------------------------

More to know !

• Quadratic equation standard form :ax²+bx-c

• $\mathtt{If \:D=b²−4ac>0}$

discriminant of the equation is positive then the equation has real and distinct roots.

• $\mathtt{If \: D=b²-4ac < 0}$

the discriminant of the quadratic equation is negative then the equation has no real roots.

• $\mathtt{If \:D=b²-4ac=0 }$

the discriminant of the equation is zero, the equation has real and equal roots.