Home
Class 12
MATHS
If p ,q in {1,2,3,4,5} , then find the n...

If `p ,q in {1,2,3,4,5}` , then find the number of equations of form `p^2x^2+q^2x+1=0` having real roots.

Text Solution

Verified by Experts

The correct Answer is:
16 equations.
`because D = q^(4) - 4p^(2) gen 0`
`=(q^(2) + 2p)(q^(2) - 2p) ge 0`
`rArr q^(2) ge 2p`
If p = 1, then q = 2, 3, 4, ,5
p = 2, then q = 2, 3, 4, ,5
p = 3, then q = 3, 4, ,5
p = 4, then q = 3, 4, ,5
p = 5, then q = 4, ,5
So, number of possible equation is 16
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.9|12 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.10|5 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.7|9 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

Similar Questions

Explore conceptually related problems

Find the number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=0.

If p and q are the roots of the equation x^(2)+px+q=0 , then

The number of real roots of the equation |x|^(2)-3|x|+2=0 is

If p ,q ,r are positive and are in A.P., the roots of quadratic equation p x^2+q x+r=0 are all real for a. |r/p-7|geq4sqrt(3) b. |p/r-7|geq4sqrt(3) c. all p and r d. no p and r

Find the maximum possible number of real roots the equation . x^5-6x^2-4x+5=0

The equation ax^(4)-2x^(2)-(a-1)=0 will have real and unequal roots if

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

Find the values of p so that the equation 2cos^2x-(p+3)cosx+2(p-1)=0 has a real solution.