`x_1a n dx_2` are the roots of `a x^2+b x+c=0a n dx_1x_2<0.` Roots of `x_1(x-x_2)^2+x_2(x-x_1)^2()_()=0` are a. real and of opposite sign b. negative c. positive d. none real

If x_1a n dx_2 are the roots of the equation e^2*x^(lnx)=x^3 with x_1> x_2, then x_1=2x_2 (b) x_1=x_2^2 (c) 2x_1=x_2^2 (d) x_1^2=x_2^3

If x_1, a n dx_2 are the roots of x^2+(sintheta-1)x-1/2(cos^2theta)=0, then find the maximum value of x_1^2+x_2^2

Find the condition if the roots of a x^2+2b x+c=0a n db x^2-2sqrt(a c )x+b=0 are simultaneously real.

If 8 and 2 are the roots of x^(2) + ax + c = 0 and 3,3 are the roots of x^(2) + dx + b = 0, then the roots of the equation x^(2) + ax + b = 0 are

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alphaa n dbetadot

If x_1 and x_2 are the real and distinct roots of a x^2+b x+c=0, then prove that lim_(n->x_1){1+"sin"(a x^2+b x+c)}^(1/(x-x_1))=e^(a(x_1-x_2))

If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are the roots of p x^2+q x+r=0then h= a. -1/2(a/b-p/q) b. (b/a-q/p) c. 1/2(b/a-q/p) d. none of these

If x=1a n dx=2 are solutions of equations x^3+a x^2+b x+c=0a n da+b=1, then find the value of bdot

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