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### High School Mathematics6.7 Problems on Roots

 Example: If one root of x2 - (a+1)x - 21 = 0 is -3, find the value of a. Solution: If the roots of ax2 + bx + c = 0 are a and b then, Sum of the roots (a + b) = -b/a = (Coefficient of x / Coefficient of x2). Product of the roots (a * b) = c/a = (constant term / coefficient of x2). Let the roots of the equation x2 - (a+1)x - 21 = 0 be a and b, one root is -3, i.e. a = -3 Sum of the roots (a + b) = a + 1 -3 + b = a + 1 Product of the roots (ab) = -21 Given that a = -3, Therefore, -3b = -21 b = 21/3 b = 7 -3 + 7 = a + 1 a = 4 - 1 a = 3 Directions: Solve the following problems. Also write at least 5 examples of your own.
 Q 1: If one root of x2 - (5+a)x + 24 = 0 is 3 find the value of a.2465 Q 2: If one root of 6x2 - (21+a)x + 25 = 0 is 5/2 find the value of a.4756 Q 3: If one root of 2x2 - (16+a)x + 25 = 0 is 5/2 find the value of a.12-1-2 Q 4: If one root of x2 - (7+a)x - 56 = 0 is -8 find the value of a.8-86-6 Q 5: If one root of 2x2 - (7+a)x - 15 = 0 is 5 find the value of a.3456 Q 6: If one root of 2x2 - (3+a)x + 6 = 0 is 2 find the value of a.3654 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!