Question

Find the quadratic polynomial, the sum and product of whose zeroes are respectively √2 and 2+ √2.

Answer 1

Answer:

k($x^{2}$ - √2x + 2 + √2) = 0

Step-by-step explanation:

Let the quadratic equation be $ax^{2} +bx + c = 0$

Lets roots be m and n

Then,

$ax^{2} +bx + c = 0$ can be expressed as ( x - m )( x - n ) = 0

m + n = $-\frac{b}{a}$

$-\frac{b}{a}$ = √2

mn = $\frac{c}{a}$

$\frac{c}{a}$ = 2 + √2

We can assume a = k ( Where k is a real number )

Then b = -√2 k

c = (2 + √2)k

Hence the quadratic equation is k$x^{2}$ + (-√2 k)x + (√2 + 2)k = 0

Which can also be written as k($x^{2}$ - √2x + 2 + √2) = 0

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