## Class 10 Maths Chapter 4 Quadratic Equations

**1 Mark Questions:**

Q1. Find the roots of the equation x2 – 3x – m (m + 3) = 0, where m is a constant. (2011OD)

Q2. If 1 is a root of the equations ay^{2} + ay + 3 = 0 and y^{2} + y + b = 0, then find the value of ab. (2012D)

Q3. If x = – 1/2 , is a solution of the quadratic equation 3x^{2} + 2kx – 3 = 0, find the value of k. (2015D)

**2 Marks Questions:**

Q1. Find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has two equal roots. (2011D, 2014OD)

Q2. Find the roots of 4x^{2} + 3x + 5 = 0 by the method of completing the squares. (2011D)

Q3. Find the value of m so that the quadratic equation mx (x – 7) + 49 = 0 has two equal roots. (2011OD)

Q4. 36x^{2} – 12ax + (a^{2} – b^{2}) = 0 (2011OD)

Q5. Find the value(s) of k so that the quadratic equation x^{2} – 4kx + k = 0 has equal roots. (2012D)

Q6. Find the value of k for which the equation x^{2} + k(2x + k – 1) + 2 = 0 has real and equal roots. (2017D)

Q7. Find the value of p for which the roots of the equation px(x – 2) + 6 = 0, are equal. (2012OD)

Q8. Solve the quadratic equation 2x^{2} + ax – a^{2} = 0 for x. (2014D)

Q9. Find the values of p for which the quadratic equation 4x^{2} + px + 3 = 0 has equal roots. (2014OD)

Q10. Solve the following quadratic equation for x: 4x^{2}– 4a^{2}x + (a^{4} – b^{4}) = 0. (2015D)

Q11. Solve the following quadratic equation for x: 9x^{2} – 6b^{2}x – (a^{4} – b^{4}) = 0 (2015D)

Q12. Solve the following quadratic equation for x: 4x^{2} + 4bx – (a^{2} – b^{2}) = 0 (20150D)

Q13. Solve the following quadratic equation for x: x^{2} – 2ax – (4b^{2} – a^{2}) = 0) (2015OD)

Q14. Find the value of p, for which one root of the quadratic equation px^{2} – 14x + 8 = 0 is 6 times the other. (20170D)

Q15. If -5 is a root of the quadratic equation 2x^{2} + px – 15 = 0 and the quadratic equation p(x^{2} + x) + k = 0 has equal roots, find the value of k. (2016OD).