Question : What is the difference between the cube and square of the common root of $x^2-8x+15=0$ and $y^2+2y-35=0$
Option 1: 76
Option 2: 100
Option 3: 294
Option 4: 318
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Correct Answer: 100
Solution : Here, $x^2-8x+15=0$ ⇒ $(x-5)(x-3)=0$ So, $x=5,3$ $y^2+2y-35=0$ ⇒ $(y-5)(y+7)=0$ So, $y=5,-7$ Here, the common root is 5. So, the difference between the cube and square of 5 $=(5^3-5^2)=125-25=100$ Hence, the correct answer is 100.
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