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|20 Videos

Similar Questions

Explore conceptually related problems

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

If p,q,in{1,2,3,4}, then find the number of equations of the form px^(2)+qx+1=0 having real roots.

let p,q varepsilon(1,2,3,4), then number of equation of the form px^(2)+qx+1=0 ,having real roots is

Let alpha, beta be the roots of x^2-x+p=0 and gamma, delta be the roots of x^2-4x+q=0 such that alpha, beta, gamma, delta are in G.P. and pge2. If a,b,c epsilon {1,2,3,4,5}, let the number of equation of the form ax^2+bx+c=0 which have real roots be r, then the minium value of p q r =

If p,q,r and s are real numbers such that pr=2(q+s), then show that at least one of the equations x^(2)+px+q=0 and x^(2)+rx+s=0 has real roots.

Show that if p,q,r and s are real numbers and pr=2(q+s) , then atleast one of the equations x^(2)+px+q=0 and x^(2)=rx+s=0 has real roots.

Consider the equation of the form x^(2)+px+q=0 , then number of such equations that have real roots and have coefficients p and q in the set {1,2,3,4,5,6} (p may be equal to q) is