A two digit number is such that the product of its digits

Question

1. Find the roots of the equation pqx² − (p − q)x − 1 = 0.

2. If α and β are roots of x²+px+q=0, then what is the value of α²+β²?

3. If one root of the equation x²+12x−k=0 is thrice the other, then the value of k is

4. If the equation 3x²−kx+4=0 has equal roots, then the values of k are

5. Using the quadratic formula, solve the equation:

a²b²x² - (4b⁴-3a⁴)x-12a²b² = 0

6. Solve for X : 

 

7. A two digit number is such that the product of its digits is 35. When 18 is added to the number, the digits interchange their places. Find the number.

8. A motor boat whose speed is 18 km/hr in still water takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream.

9. The roots of the equation x²+x−(p+1)(p+2)=0 are

10. If -2 and 5 are roots of the equation 2x²−3mx+5n=0, then what are the values of m and n ?