CAT Quadratic Equations previous year questions

13 Quadratic Equations questions from CAT 2021–2025 (Quant), each with its answer and a step-by-step solution.

• Q7The number of non-negative integer values of k for which the quadratic equation x²-5x+k=0 has only integer roots, isCAT 2025 Slot 1 · Quant · Quadratic Equations
• Q16The equations 3x²-5x+p=0 and 2x²-2x+q=0 have one common root. The sum of the other roots of these two equations isCAT 2025 Slot 2 · Quant · Quadratic Equations
• Q20If the equations x²+mx+9=0 , x²+nx+17=0 and x²+ ( m+n )x+35=0 have a common negative root, then the value of ( 2m+3n )…CAT 2024 Slot 1 · Quant · Quadratic Equations
• Q16The roots α , β of the equation 3x²+lambda x-1=0 , satisfy (1)/(α²)+(1)/(β²)=15 . The value of (α³+β³ )² , isCAT 2024 Slot 2 · Quant · Quadratic Equations
• Q6Let α and β be the two distinct roots of the equation 2x²-6x+k=0 , such that ( α +β ) and α β are the distinct roots…CAT 2023 Slot 1 · Quant · Quadratic Equations
• Q7Let k be the largest integer such that the equation ( x-1 )²+2kx+11=0 has no real roots. If y is a positive real…CAT 2023 Slot 2 · Quant · Quadratic Equations
• Q5A quadratic equation x²+bx+c=0 has two real roots. If the difference between the reciprocals of the roots is (1)/(3) ,…CAT 2023 Slot 3 · Quant · Quadratic Equations
• Q5Let a , b , c be non-zero real numbers such that b²<4ac , and f ( x )=ax²+bx+c . If the set S consists of all integers…CAT 2022 Slot 1 · Quant · Quadratic Equations
• Q20Let f ( x ) be a quadratic polynomial in x such that f ( x )≥ 0 for all real numbers x . If f ( 2 )=0 and f ( 4 )=6 ,…CAT 2022 Slot 2 · Quant · Quadratic Equations
• Q1Suppose k is any integer such that the equation 2x²+kx+5=0 has no real roots and the equation x²+ ( k-5 )x+1=0 has two…CAT 2022 Slot 3 · Quant · Quadratic Equations
• Q14If ( 3+2√2 ) is a root of the equation ax²+bx+c=0 , and ( 4+2√3 ) is a root of the equation ay²+my+n=0 , where a , b ,…CAT 2022 Slot 3 · Quant · Quadratic Equations
• Q5If r is a constant such that |x²-4x-13 |=r has exactly three distinct real roots, then the value of r isCAT 2021 Slot 1 · Quant · Quadratic Equations
• Q19Suppose one of the roots of the equation ax²-bx+c=0 is 2+√3 , where a , b and c are rational numbers and a≠ 0 . If…CAT 2021 Slot 2 · Quant · Quadratic Equations