Bissoy.com
Doctors Medicines MCQs Q&A

If one root of the equation ax2 + bx + c = 0 where a, b, c are integers is (√5 + 3), then the other root is

If one root of the equation ax2 + bx + c = 0 where a, b, c are integers is (√5 + 3), then the other root is Correct Answer 3 - √5

Concept:

  • In a quadratic equation surd or irrational roots occur in conjugate pairs.
  • For example if one of the root of a quadratic equation is α + √β then the other root will be its conjugate that is α − √β

 

Calculation:

If one of the root of the quadratic equation ax2 + bx + c = 0 is √5 + 3 or 3 + √5 then the other root will be its conjugate that is 3 − √5

So, other root is 3 − √5

 

/2a = √5

So, We can write the roots as 

x = 3 ± √5 

So, The other root is 3 - √5.

Related Questions

In quadratic equations aX2 + bX + c = 0 and dY2 + eY + f = 0, a, b and c are the coefficient of X2, X and constant term of aX2 + bX + c = 0 while d, e and f (are integers) and are the coefficient of Y2, Y and constant term of equation dY2 + eY + f = 0. If the ratio of sum of a and b together to the sum of b and c together is 11 : 6, a : b = 6 : 5, b2 = 4a + c, f2 = e + d – 3, d : e = 3 : 4, and e = 3f + 1 then find a quartic equation in Z(variable) whose roots are the roots of given equations.
Which of the following is true? A: If the sum of cube of three numbers is thrice the product of the three numbers, then the sum of three numbers will be non-zero. B: For quadratic equation ax2 + bx + c = 0, If b2 < 4ac, then the given equation has only one real root. C: In the equation, x2 – (a + b)x + ab = 0, the roots of this equation will be ‘a’, ‘b’.
Consider the statements given below: A: Sum of roots of a quadratic equation ax2 + bx + c = 0 is (c/a). B: If one root of a quadratic equation is (p + qi), then root must be (q + pi). C: Roots of the equation 3x2 + 4x = 5 are all real. Which of the statement(s) is/are TRUE?
Let Z be the set of real integers and R the set of real numbers. The sampling process may be viewed as partitioning the x-y plane into a grid, with the central coordinates of each grid being from the Cartesian product Z2, that is a set of all ordered pairs (zi, zj), with zi and zj being integers from Z. Then, f(x, y) is a digital image if (x, y) are integers from Z2 and f is a function that assigns a gray-level value (that is, a real number from the set R) to each distinct coordinate pair (x, y). What happens to the digital image if the gray levels also are integers?
A, B, C, D and E are five different integers. When written in the ascending order of values, the difference between any two adjacent integers is 4. D is the greatest and A is the least. B is greater than E but less than C. The sum of the integers is equal to E. What is the positive difference between the lowest and the highest integers?
The average of 4 positive integers is 59. The highest integer is 83 and the lowest integer is 29. The difference between the remaining two integers is 28. Which of the following integers is higher of the remaining two integers ?
The average of 5 positive integers is 60. If the average of 3 of these integers is 67, what is the greatest possible value that one of the other two integers can have?
Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
When subtracting the square root of the square root of 625 from the square root of the square root of 1296, which of the following number is square root of the difference?
Which of the following represents the correct matching set.   Type of root   Example a) Taproot root i) Banyan tree b) Adventitious root ii) Carrot c) Prop root iii) Sugarcane d) Stilt root iv) Sweet potato