CT 22: Quadratic Equaiton – II

1.If the equation (1 + t²)x² +2tcx + (c² − a²) = 0 has equal roots then which of the following is true?

2. If the zeroes of the quadratic polynomial ax² + bx + c ≠ 0 are equal, then

3. The least positive value of 'k' for which the equation x² + kx + 9 = 0 has real roots, is

4. If the equation x² - bx + 9 = 0 does not possess real roots, then

5. The equation (x² + 1)² - x² = 0 has

6. Under what condition the roots of equations ax² + 2bx + c = 0 and bx² - 2ac−−√x2acx + b = 0 are simultaneously real ?

7. If the roots of the quadratic equation x² – (k + 2)x + 121 = 0 are equal, then positive value of k?

8. If a, b, c are in HP, then the equation a(b - c)x² + b(c - a)x + c(a - b) = 0

9. The quadratic equation which has real and equal roots 3/5 is :

10. Find the nature of roots of 2(p + q)²x² + 2(p + q)x + 1 = 0