If the sum of the roots of the equation `1/(x+a)+1/(x+b)=1//c` is zero, the prove that the product of the root is `(-1/2)(a^2+b^2)dot`

If the sum of roots of the quadratic equation is 1/(x + p) + 1/(x + q) = 1/r is zero, show that the product of the roots is - ((p^(2) +q^(2))/2)

Determine the nature of the roots of the equation 2x^(2) + x - 1 = 0

If the difference of the roots of the equation 2x^(2)-(a+1)x+a-1=0 is equal to their product then prove that a=2

If the product of the roots of the equation (a+1)x^2+(2a+3)x+(3a+4)=0i s2, then find the sum roots.

If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b are roots of the equation (x-c)(x-d)+k=0.

If the sum of the roots of the equation (a+1)x^(2)+(2a+3)x+(3a+4)=0 , is -1.Find its product.

If the difference of the roots of the equation 2x^(2) - (a +1) x + a -1 = 0 is equal to their product, then prove that a = 2.

If the sum of the roots of the quadratic equation a x^2+b x+c=0 is equl to the sum of the squares of their reciprocals, then prove that a/c , b/a a n d c/b are in H.P.

If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alpha^3-3alpha is the other root.

If both roots of the equation a(x^2-1)+x+c are imaginary and c gt -1 then