Question

Write the quadratic equation that has roots (√3+1)/2 and (√3 -1 )/2, if its coefficient with x^2 is equal to:

a) 1
b) 5
c) - 1/2
d) √3

Answer 1

Answer:

The equation is: $x^2-x+\frac{1}{2}$

(A)$x^2-x+\frac{1}{2}=0$

(B)$5x^2-5x+\frac{5}{2}=0$

(C) $-\frac{1}{2}$

$-\frac{1}{2}x^2+\frac{1}{2}x-\frac{1}{4}=0$

d) √3

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

Step-by-step explanation:

If the roots of the quadratic equation are: $\frac{\sqrt{3}+1}{2} and \frac{\sqrt{3}-1}{2}$

This means:

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

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

If a=0 or b=0, then ab=0

Therefore:

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

Therefore the coefficient of $x^2$  here is 1.

b) To make 5 the coefficient of $x^2$

Simply multiply $x^2-x+\frac{1}{2}=0$ by 5

This gives: $5x^2-5x+\frac{5}{2}=0$

c) $-\frac{1}{2}$

To make $-\frac{1}{2}$ the coefficient of $x^2$

Simply multiply $x^2-x+\frac{1}{2}=0$ by $-\frac{1}{2}$

This gives: $-\frac{1}{2}x^2+\frac{1}{2}x-\frac{1}{4}=0$

d) √3

To make  $\sqrt{3}$ the coefficient of $x^2$

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

This gives: $(\sqrt{3}) x^2-x\sqrt{3}+\frac{\sqrt{3}}{2}=0$