# CAT 2023 Question Paper | Quant Slot 1

###### CAT Previous Year Paper | CAT Quant Questions | Question 6

CAT 2023 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 6 : Let $$alpha$ and $$beta$ be the two distinct roots of the equation $2 x^2-6 x+k=0$, such that $$$alpha+\beta$$ and $$alpha \beta$ are the distinct roots of the equation $x^2+p x+p=0$. Then, the value of $8$k-p$$ is

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$$alpha$ and $$beta$ are the distinct roots of the equation $2 x ^ { 2 } - 6 x + k = 0$. Therefore, $\alpha + \beta = \frac { -$ - 6$ } { 2 } = 3$
$$alpha $cdot \beta = \frac { k } { 2 }$ We know that $$ $alpha + \beta$$ and $$ $alpha , $beta$$ are the roots of the equation: $x ^ { 2 } + p x + p = 0$ $$ $alpha + $beta$ +$ $alpha $cdot \beta$ = 3 + $frac { k } { 2 } = \frac { -$ p$ } { 1 } = - p$