The graph of the quadratic trinomial `u=a x^2+b x+c` has its vertex at (4, -5) and two x-intercepts, one positive and one negative. Which of the following holds good? `a >0` b. `b<0` c. `<0` d. `8a=b`

If the quadratic equation a x^2+b x+c=0(a >0) has sec^2thetaa n dcos e c^2theta as its roots, then which of the following must hold good? (a.) b+c=0 (b.) b^2-4a cgeq0 (c.) c ccgeq4a (d.) 4a+bgeq0

If a ,b in R ,a!=0 and the quadratic equation a x^2-b x+1=0 has imaginary roots, then (a+b+1) is a. positive b. negative c. zero d. Dependent on the sign of b

A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=x has no real roots. Prove that in this case equation P(P(x))=x has no real roots either.

If the equation x^2=a x+b=0 has distinct real roots and x^2+a|x|+b=0 has only one real root, then which of the following is true? b=0, a >0 b. b=0, a 0, a >0

Let f(x)=a x^2+b x+c be a quadratic expression having its vertex at (3, -2) and value of f(0)=10. find f(x)

If the equation sin^2 x-a sin x + b = 0 has only one solution in (0, pi) then which of the following statements are correct?

Find the condition if the equation 3x^2+4a x+b=0 has at least one root in (0,1)dot

If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are the roots of x^2-r x+s=0 , then the equation x^2-4q x+2q^2-r=0 has always. A. one positive and one negative root B . two positive roots C . two negative roots D . cannot say anything

Draw the graph of y=x^(2)-3x -4 , find its line of symmetry, vertex, x intercepts

All the value of k for which the quadratic polynomial f(x)=-2x^2+k x+k^2+5 has two distinct zeroes and only one of them satisfying 0 < x < 2 ,lie in the interval (a ,b) The value of (a+10 b) is