If `a ,b ,p ,q` are nonzero real numbers, then how many comman roots would two equations `2a^2x^2-2a b x+b^2=0a n dp^2x^2+2p q x+q^2=0` have?

If p and q are the roots of the equation x^(2)+px+q=0 , then

If the abscissa and ordinates of two points Pa n dQ are the roots of the equations x^2+2a x-b^2=0 and x^2+2p x-q^2=0 , respectively, then find the equation of the circle with P Q as diameter.

Show that , if p,q,r are rational , the roots of the equation x^2-2px+p^2-q^2+2pr-r^2=0 are rational .

The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are

If the normals to the parabola y^2=4a x at three points (a p^2,2a p), and (a q^2,2a q) are concurrent, then the common root of equations P x^2+q x+r=0 and a(b-c)x^2+b(c-a)x+c(a-b)=0 is (a) p (b) q (c) r (d) 1

If aa n db are positive numbers and eah of the equations x^2+a x+2b=0a n dx^2+2b x+a=0 has real roots, then the smallest possible value of (a+b) is_________.

The solution set of the equation pqx^(2)-(p+q)^(2)x+(p+q)^(2)=0 is

If one root is square of the other root of the equation x^2+p x+q=0 then the relation between p and q is

Using quadratic formula solve the following equations. p^(2)x^(2)+(p^(2)-q^(2))x-q^(2)=0

If alpha is a real root of the quadratic equation a x^2+b x+c=0a n dbeta ils a real root of -a x^2+b x+c=0, then show that there is a root gamma of equation (a//2)x^2+b x+c=0 whilch lies between alpha & beta