Question

form a quadratic equation whose roots are 3+√7 , 3-√7

Answer 1

x²-3x+2=0
.
.
by the formula
x²-(sum of roots)x +(product of roots)=0

Answer 2

A quadratic equation whose zeroes are $3+\sqrt7$ and $3-\sqrt7$ is $x^2-6x+2=0$

Step-by-step explanation:

To find : A quadratic polynomial whose zeroes are $3+\sqrt7$ and $3-\sqrt7$ ?

Solution :

The roots of the quadratic equation $ax^2+bx+c=0$ are $\alpha$  and $\beta$.

So, Let $\alpha=3+\sqrt7$ and $\beta=3-\sqrt7$

The formula to get the equation is

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

Substitute the values,

$x^2-(3+\sqrt7+3-\sqrt7)x+(3+\sqrt7)(3-\sqrt7)=0$

$x^2-6x+3^2-(\sqrt7)^2=0$

$x^2-6x+9-7=0$

$x^2-6x+2=0$

Therefore, a quadratic equation whose zeroes are $3+\sqrt7$ and $3-\sqrt7$ is $x^2-6x+2=0$.

#Learn more

Write quadratic equation whose roots are  2 and 4.​

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