The quadratic equation `x^2+m x+n=0` has roots which are twice those of `x^2+p x+m=0a dm ,na n dp!=0.` The n the value of `n//p` is _____.

The quadratic equation whose roots are twice the roots of 2x^(2)-5x+2=0 is

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0a n dalpha^2,beta is the roots of quadratic equation x^2-q x+8=0 , then the value of rifr/8 is the arithmetic mean of pa n dq , is (83)/2 b. 83 c. (83)/8 d. (83)/4

The quadratic polynomial p(x) has the following properties: p(x)geq0 for all real numbers, p(1)=0a n dp(2)=2 . Find the value of p(3) is__________.

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

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0

If (1-p) is a root of quadratic equation x^(2)+px+(1-p)=0 then its roots are

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot

If x satisfies x^(2)-2x cos theta +1=0 , then the value of x^(n)+((1)/(x^n)) is

Let alpha,beta be the roots of the equation x^2-p x+r=0a n dalpha//2,2beta be the roots of the equation x^2-q x+r=0. Then the value of r is 2/9(p-q)(2q-p) b. 2/9(q-p)(2q-p) c. 2/9(q-2p)(2q-p) d. 2/9(2p-q)(2q-p)

Which of the following is not the quadratic equation whose roots are cos e c^2thetaa n dsec^2theta? x^2-6x+6=0 (b) x^2-7x+7=0 x^2-4x+4=0 (d) none of these