If the sum of the roots of the equation \(\dfrac{1}{2x+p} + \dfrac{1}{2x+q} = \dfrac{1}{r}\) is zero, then what is \(r\) equal to?
\(\dfrac{p+q}{2}\)
Combining the fractions gives \(r(4x+p+q) = (2x+p)(2x+q) = 4x^2+2x(p+q)+pq\), i.e. \(4x^2+[2(p+q)-4r]x+[pq-r(p+q)]=0\). The sum of roots is zero, so \(2(p+q)-4r=0\), giving \(r=\dfrac{p+q}{2}\).
Similar Questions
If the roots of the equation 4x 2- (5k + 1)x + 5k = 0 differ by unity, then which one of the following is a possible value of k?
For how many quadratic equations, the sum of roots is equal to the product of roots?
If α and β are the roots of the equation 4x 2+ 2x - 1 = 0, then which one of the following is correct?
What is sin (α + β) sec α sec β equal to?
What is tan (α + β) equal to?
If k is one of the roots of the equation x(x + 1) + 1 = 0, then what is its other root?
The sum of the roots of the equation ax 2+ x + c = 0 (where a and c are non-zero) is equal to the sum of the reciprocals of their squares. Then a, ca 2, c 2are in
If cot α and cot β are the roots of the equation x 2+ bx + c = 0 with b ≠ 0, then the value of cot (α + β) is
Let α and β (α > β) be the roots of the equation x 2- 8x + q = 0. If α 2- β 2= 16, then what is the value of q?
If cot α and cot β are the roots of the equation x 2- 3x + 2 = 0, then what is cot (α + β) equal to ?
Important Questions from Sum and Product of Roots
If the roots of the equation 4x 2- (5k + 1)x + 5k = 0 differ by unity, then which one of the following is a possible value of k?
For how many quadratic equations, the sum of roots is equal to the product of roots?
If α and β are the roots of the equation 4x 2+ 2x - 1 = 0, then which one of the following is correct?
What is sin (α + β) sec α sec β equal to?
What is tan (α + β) equal to?
