Question

Find a quadratic polynomial the sum and product of whose zeroes are root 3 and 1 upon root 3 respectively

Answer 1

Answer:

The answer is , $\sqrt{3}x^2 - 3x +1 =0$

Step-by-step explanation:

Given :- Sum of the roots =α+β =  $\sqrt{3}$ , product of the roots = α*β = $\frac{1}{\sqrt{3} }$

To find :- quadratic equation .

Solution :-

1) we know that general quadratic equation is $ax^2 + bx +c = 0$----(1)

divide the above equation by 'a' ,

we get , $x^2 + \frac{b}{a}x+ \frac{c}{a} = 0$ ------(2)

2) let , α and β be the roots of the equation ,

given that , α+β = $\sqrt{3}$ , α*β = $\frac{1}{\sqrt{3} }$ ,

also , we know α+β = $-\frac{b}{a}$ , α*β = $\frac{c}{a}$ .

3) substituting the values in eqn. (2)

we get ,

$x^2 - \sqrt{3} x + \frac{1}{\sqrt{3} } = 0 \\ \sqrt{3}x^2 - 3x + 1 = 0$

4) The answer is , $\sqrt{3}x^2 - 3x +1 = 0$

#SPJ2

Answer 2

Step-by-step explanation:

Quadratic polynomial= k(x²- (alfa+ bita)x alfa× bita)

= k (x² (√3)x + l/√3)

= k (x² - √3x - 1/√3)

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