CT 16: Quadratic Equation - II

Welcome to your CT 16: Quadratic Equation - II

Question no 1

1.If roots of quadratic equation ax² + 2bx + c = 0 are equal then

A. a, b, c in A.P

B. a, b, c in G.P

C. a, b, c in H.P

D. None of these

Question no 2

2. If the equation x² - (2 + m)x + (m² - 4m + 4) = 0 in x has equal roots, then the values of m as

A. 2/3, 1

B. 2/3, 6

C. 0, 1

D. 0, 2

Question no 3

3. Find the values of k for which the equation x² − 4x + k = 0 has distinct real roots.

A. k = 4

B. k < 4

C. k > 4

D. k = 6

Question no 4

4. For equation x2 - px + q = 0,

I: If the difference of the roots is unity, then p2 + 4q2 = (1 + 2q)²

II: Roots are equal if p = 4q.

Which of the following statement(s) is/are correct.

A. Only I

B. Only II

C. Both I and II

D. None

Question no 5

5. Find the value of k for which the equation x2 + 5kx + 16 = 0 has no real roots?

A. 0 < k < 8/3

B. k > 8/7

C. - 8/3 < k < 0

D. - 8/5 < k < 8/5

Question no 6

6. How many real roots does the equation √x+9=x−3 have?

A. Only one

B. Only two

C. Only three

D. None

Question no 7

7. For which value of c will the quadratic equation ax2 + bx + c = 0 have the same roots?

A. b²/a

B. b²/4a

C. a²/b

D. a²/4b

Question no 8

8. Determine the nature of the roots of the equation 2x² + 5x + 5 = 0

A. imaginary and distinct

B. real and equal

C. imaginary and equal

D. real and distinct

Question no 9

9. If the roots of the equation x² - 2px + 8p - 15 = 0 are equal, find the possible values of p.

A. 3 or 5

B. 2 or 5

C. 3 or 4

D. 2 or 4

Question no 10

10. Find the nature of roots of quadratic equation:-

2x²−3√2x+9/4=0

A. Real and equal roots

B. Real and unequal.

C. Imaginary roots

D. Cannot determine

CT 16: Quadratic Equation – II

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