CAT 2022 Linear and Quadratic Equations Question (Hard)

Question

If is a root of the equation , and is a root of the equation , where and are integers, then the value of is

Accepted Answer

Step 1 Identify the given information - is a root of - is a root of - All coefficients are integers Need to find Step 2 Find conjugate roots Since coefficients are integers and we have irrational roots, the conjugate roots must also be roots - For first equation is also a root - For second equation

CAT 2022

Quantitative

Linear and Quadratic Equations

Hard

If $(3+2 \sqrt{2})$ is a root of the equation $a x^2+b x+c=0$ , and $(4+2 \sqrt{3})$ is a root of the equation $a y^2+m y+n=0$ , where $a, b, c, m$ and $n$ are integers, then the value of $\left(\frac{b}{m}+\frac{c-2 b}{n}\right)$ is

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