A quadratic equation `f(x)=a x^2+b x+c=0` has positive distinct roots reciprocal of each other. Which one is correct? `f^(prime)(1)=0` (b) `af^(prime)(1)<0` `c!=b` (d) `a b c!=0`

A quadratic equation f(x)=a x^2+b x+c=0(a != 0) has positive distinct roots reciprocal of each ether. Then

If quadratic equation f(x)=x^(2)+ax+1=0 has two positive distinct roots then

If one root of the quadratic equation 3x^(2)-10x+k=0 is reciprocal of the other, find the value of k.

If equation f(x)=x^4-a x^3+b x^2-c x+420 have all roots integer and greater than 1. Given that f(4)=0, then f(-4)=0 (b) f(8)=60 f^(prime)(4)=3 (d) f^(prime)(3)=-8

Consider quadratic equations x^2-ax+b=0 and x^2+px+q=0 If the above equations have one common root and the other roots are reciprocals of each other, then (q-b)^2 equals

If quadratic equation x^(2)-(m+1)x+6=0 has one root as x=3 , find the value of m and the other root of the equations.

If f(x)=(x+3)/(5x^2+x-1) and g(x)=(2x+3x^2)/(20+2x-x^2) such that f(x) and g(x) are differentiable functions in their domains, then which of the following is/are true (a) 2f^(prime)(2)+g^(prime)(1)=0 (b) 2f^(prime)(2)-g^(prime)(1)=0 (c) f^(prime)(1)+2g^(prime)(2)=0 (d) f^(prime)(1)-2g^(prime)(2)=0

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x) a tx=a is also the normal to y=f(x) a tx=b , then there exists at least one c in (a , b) such that (a)f^(prime)(c)=0 (b) f^(prime)(c)>0 (c) f^(prime)(c)<0 (d) none of these

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x)a tx=a is also the normal to y=f(x)a tx=b , then there exists at least one c in (a , b) such that f^(prime)(c)=0 (b) f^(prime)(c)>0 f^(prime)(c)<0 (d) none of these

If the equation a x^2+2x+a=0 has two distinct roots, if (a) a=+-1 (b) a=0 (c) a=0,\ 1 (d) a=-1,\ 0