The equation px2 + qx+ r= 0 (where p, q, r, all are positive) has distinct real roots a and b. Which one of the following is correct?a)a 0, b 0b)a

Question

The equation px2 + qx+ r= 0 (where p, q, r, all are positive) has distinct real roots a and b. Which one of the following is correct?a)a > 0, b > 0b)a < 0, b < 0c)a > 0, b < 0d)a < 0, b > 0Correct answer is option 'B'. Can you explain this answer?

Answer

The discriminant of the quadratic equation is given by b^2 - 4ac. If the discriminant is positive, it means there are two distinct real roots.

In this case, the discriminant is given by q^2 - 4pr. Since p, q, and r are all positive, q^2 - 4pr will also be positive. Therefore, the quadratic equation has two distinct real roots.

Therefore, the correct answer is a) 'a and b are both real numbers.'

Similar Defence Doubts

Consider the following2x2 + 3x - α- 0 has roots -2 and βwhile the equation x2 - 3mx + 2m2 = 0 has both roots positive, where α> 0 and β > 0. 39.Q. What is the value of α?

Consider the following2x2+ 3x - α- 0 has roots -2 and βwhile the equation x2- 3mx + 2m2= 0 has both roots positive, where α> 0 and β > 0. 39.If β, 2 , 2m are in GP, then what is the value of

Consider the following statements in respect of the given equation:(x2 + 2)2 + 8x2= 6x(x2+ 2)1. All the roots of the equation are complex.2. The sum of all the roots of the equation is 6.Q. Which of the above statements is/are correct?

The roots of the equation x2 8x + 16 = 0

The roots of the equation x2—8x+ 16 = 0

Top Courses for Defence

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams