Question

Find a quadratic polynomial, the sum and product of whose zeroes are $\sqrt{2} and \frac{-3}{2}$,

respectively. Also find its zeroes.

Answer 1

Step-by-step explanation:

Sum = \sqrt{2}

2

, Product = \frac{1}{3}

3

1

General form of a quadratic equation => x^2 - (a + B)x + aBx

2

−(a+B)x+aB

Note: a & B are zeroes of the polynomial.

So the polynomial is x ^2 - \sqrt 2x + 1/3x

2

−

2

x+1/3

It can be re-written as: 3x^2 - 3 \sqrt 2x + 13x

2

−3

2

x+1

Now we should fine the zeroes!

3x^2 - 3 \sqrt 2x + 13x

2

−3

2

x+1

By using quadratic formula, we get

\frac{1}{\sqrt2} +_- \frac {1}{\sqrt 6}

2

1

+

−

6

1