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(1) If ‘m’ and ‘n’ are the roots of the equation x2 − 6x + 2 = 0 find the value of(i) (m + n) mn(ii) (2) If ‘a’ and ‘b’ are the roots of the equation 3m2 = 6m + 5, find the value of(i) (ii) (a + 2b) (2a + b)(3) If ‘p’ and ‘q’ are the roots of the equations 2a2 − 4a + 1 = 0, find the value of(i) (p + q)2 + 4pq(ii) p3 + q3(4) From the quadratic equation whose roots are (5) Find the value of ‘k’ so that the equation x2 + 4x + (k + 2) = 0 has one root equal to zero.(6) Find the value of ‘q’ so that the equation 2x2 − 3qx = 5q = 0 has one root which is twice the other.(7) Find the value of ‘p’ so that the equation 4x2 − 8px + 9 = 0 has roots whose difference is 4.(8) If one root of the equations x2 + px + q = 0 is 3 times the other prove that 3p2 = 16q |
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Answer» (1) If ‘m’ and ‘n’ are the roots of the equation x2 − 6x + 2 = 0 find the value of (i) (m + n) mn (ii) (2) If ‘a’ and ‘b’ are the roots of the equation 3m2 = 6m + 5, find the value of (i) (ii) (a + 2b) (2a + b) (3) If ‘p’ and ‘q’ are the roots of the equations 2a2 − 4a + 1 = 0, find the value of (i) (p + q)2 + 4pq (ii) p3 + q3 (4) From the quadratic equation whose roots are (5) Find the value of ‘k’ so that the equation x2 + 4x + (k + 2) = 0 has one root equal to zero. (6) Find the value of ‘q’ so that the equation 2x2 − 3qx = 5q = 0 has one root which is twice the other. (7) Find the value of ‘p’ so that the equation 4x2 − 8px + 9 = 0 has roots whose difference is 4. (8) If one root of the equations x2 + px + q = 0 is 3 times the other prove that 3p2 = 16q |
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