Aspire Faculty ID #18359 · Topic: AMU MCA 2016 · Just now
AMU MCA 2016

The only integral root of the equation $\left|\matrix{2 - y & 2 & 3 \cr 2 & 5 - y & 6 \cr 3 & 4 & 10 - y}\right| = 0$ is

Solution

Expand determinant: $= (2-y)\left[(5-y)(10-y) - 24\right] - 2\left[2(10-y) - 18\right] + 3\left[8 - 3(5-y)\right]$ Simplify: $= (2-y)(y^2 -15y +26) + 4y -4 + 9y -21$ $= -y^3 +17y^2 -69y +52 + 13y -25$ $= -y^3 +17y^2 -56y +27$ $= 0$ Try integer root: $y=3$ $-27 +153 -168 +27 = 0$ ✔
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