wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If α and β are two real roots of the equation x3 - p x2 + qx + r = 0 satisfying the relation αβ + 1 = 0, then find the value of r2 + pr + q.


__

Open in App
Solution

Solution: For x3 + p x2 + qx + r = 0

Sum of the roots α + β + γ = -p _______(1)

αβ + βγ + γα = q ________(2)

αβγ = -r _________(3) {Given αβ = -1}

From equation 3 (-1)γ = -r

γ = r

Substituting γ in equation 2

-1 + (α + β)r = q

α + β = q+1r _________(4)

Substitute α + β+ γ = -p

q+1r + r = -p

q + 1 + r2 = -pr

r2 + pr + q + 1 = 0

r2 + pr + q = -1


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometric Progression
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon