Home
Class 12
MATHS
Consider the cubic equation x^3 +px^2 +q...

Consider the cubic equation `x^3 +px^2 +qx +r=0`, where p, q, r are real numbers, which of the following statement is correct?

Text Solution

Verified by Experts

`F(x)=x^3+px^2+qx+r`
`F'(x)=3x^2+2p+q`
`D=4p^2-12q`
`=4(p^2-3q)`
`=(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Consider the cubic equation x^(3)+ax^(2)+bx+c=0, where a,b,c are real numbers,which of the following statements is correct?

If the equations x^(2) -px +q=0 and x^(2)+qx-p=0 have a common root, then which one of the following is correct?

If px^(2) + qx + r = p ( x-a) ( x-B),and p^(3) + pq + r = 0 , p,q and r being real numbers, then which of the following is not possible?

If p, q, r each are positive rational number such tlaht p gt q gt r and the quadratic equation (p + q - 2r)x^(2) + (q + r- 2p)x + (r + p - 2q) = 0 has a root in (-1 , 0) then which of the following statement hold good? (A) (r + p)/(q) lt 2 (B) Both roots of given quadratic are rational (C) The equation px^(2) + 2qx + r = 0 has real and distinct roots (D) The equation px^(2) + 2qx + r = 0 has no real roots

If p, q, r each are positive rational number such tlaht p gt q gt r and the quadratic equation (p + q - 2r)x^(2) + (q + r- 2p)x + (r + p - 2q) = 0 has a root in (-1 , 0) then which of the following statement hold good? (A) (r + p)/(q) lt 2 (B) Both roots of given quadratic are rational (C) The equation px^(2) + 2qx + r = 0 has real and distinct roots (D) The equation px^(2) + 2qx + r = 0 has no real roots

The equation Px^(2) + qx + r = 0 (where p, q, r, all are positive ) has distinct real roots a and b .