CAT 2021 Slot 2 QA Question 15: Suppose one of the roots of the equation $ax^2 - bx + c = 0$ is $2 + \sqrt{3}$, where $a, b$ and $c$ are rational numbers and $a
e 0$. If $b = c^3$ then $\left|a ight|$ equals

Question

Suppose one of the roots of the equation $ax^2 - bx + c = 0$ is $2 + \sqrt{3}$, where $a, b$ and $c$ are rational numbers and $a 
e 0$. If $b = c^3$ then $\left|aight|$ equals

Accepted Answer

Since the coefficients are rational and one root is $2 + \sqrt{3}$, the conjugate $2 - \sqrt{3}$ is the other root.

For $ax^2 - bx + c = 0$,
$	ext{Sum of roots} = \dfrac{b}{a}$
$	ext{Product of roots} = \dfrac{c}{a}$

$(2+\sqrt{3})+(2-\sqrt{3})=4$
$\dfrac{b}{a}=4$
$b=4a$

$(2+\sqrt{3})(2-\sqrt{3}

Suppose one of the roots of the equation ax2−bx+c=0ax^2 - bx + c = 0ax2−bx+c=0 is 2+32 + \sqrt{3}2+3​, where a,ba, ba,b and ccc are rational numbers and a≠0a \ne 0a=0. If b=c3b = c^3b=c3 then ∣a∣\left|a\right|∣a∣ equals

Suppose one of the roots of the equation $ax^2 - bx + c = 0$ is $2 + \sqrt{3}$ , where $a, b$ and $c$ are rational numbers and $a \ne 0$ . If $b = c^3$ then $\left|a\right|$ equals