RD Sharma Chapter 4 : Quadratic Equation – Exercise 4.1 Solutions
- Which of the following are quadratic equations?
(i) x² + 6x – 4 = 0 (ii) √3x² – 2x + 1/2 = 0
(iii) x² + 1/x² = 5 (iv) x – 3/x = x²
(v) 2x² – √3x + 9 = 0 (vi) x² – 2x – √x – 5 = 0
(vii) 3x² – 5x + 9 = x² – 7x + 3 (viii) x + 1/x = 1
(ix) x² – 3x = 0 (x) (x + 1/x)² = 3(x + 1/x) + 4
(xi) (2x + 1)(3x + 2) = 6(x – 1)(x – 2) (xii) x + 1/x = x², x ≠ 0
(xiii) 16x² – 3 = (2x + 5)(5x – 3) (xiv) (x + 2)³ = x³ – 4
(xv) x(x + 1) + 8 = (x + 2)(x – 2) Watch Solution
- In each of the following, determine whether the given values are solutions of the given equation or not:
(i) x² – 3x + 2 = 0, x = 2, x = –1 Watch Solution
(ii) x² + x + 1 = 0, x = 0, x = 1 Watch Solution
(iii) x² – 3√3x + 6 = 0, x = √3, x = –2√3 Watch Solution
(iv) x + 1/x = 13/6, x = 5/6, x = 4/3 Watch Solution
(v) 2x² – x + 9 = x² + 4x + 3, x = 2, x = 3 Watch Solution
(vi) x² – √2x – 4 = 0, x = –√2, x = –2√2 Watch Solution
(vii) a²x² – 3abx + 2b² = 0, x = a/b, x = b/a Watch Solution
- In each of the following, find the value of k for which the given value is a solution of the equation:
(i) 7x² + kx – 3 = 0, x = 2/3 Watch Solution
(ii) x² – x(a + b) + k = 0, x = a Watch Solution
(iii) kx² + √2x – 4 = 0, x = √2 Watch Solution
(iv) x² + 3ax + k = 0, x = –a Watch Solution
- Determine, if 3 is a root of the equation given below:
√(x² – 4x + 3) + √(x² – 9) = √(4x² – 14x + 16) Watch Solution
- If x = 2/3 and x = –3 are the roots of the equation ax² + 7x + b = 0, find the values of a and b. Watch Solution