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

Question

QUADRATIC EQUATIONS

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:

a² b² x² - (4b⁴ -3a⁴ )x-12a²b² = 0

6. Solve for x : (4x-3) / (2x+1) - 10(2x+1) / (4x-3)= 3,

x # - 1/2,3/4

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?